SPECTROSCOPY OF NEUTRON UNBOUND STATES IN 24O AND 23N.

By

Michael David Jones

A DISSERTATION

Submitted toMichigan State University

in partial fulfillment of the requirementsfor the degree of

Physics – Doctor of Philosophy.

2015

ABSTRACT

SPECTROSCOPY OF NEUTRON UNBOUND STATES IN 24O AND 23N.

By

Michael David Jones

Unbound states in 24O and 23N were populated from an 24O beam at 83.4 MeV/u via

inelastic excitation and proton knockout on a liquid deuterium target. Using the MoNA-

LISA-Sweeper setup, the decay of each nucleus could be fully reconstructed. The two-body

decay energy of 23N exhibits two prominent peaks at E = 100±20 keV and E = 960±30 keV

with respect to the neutron separation energy. However, due to the lack of γ-ray detection,

a definitive statement on the structure of 23N could not be made. Shell model calculations

with the WBP and WBT interactions lead to several interpretations of the spectrum. Both

a single state at 2.9 MeV in 23N, or two states at 2.9 MeV and 2.75 MeV are consistent with

the shell model and data.

In addition, a two-neutron unbound excited state of 24O, populated by (d, d′), was ob-

served with a three-body excitation of E = 715 ± 110 (stat) ±45 (sys) keV, placing it at

E = 7.65 ± 0.2 MeV with respect to the ground state. Three-body correlations for the de-

cay of 24O →22O + 2n show clear evidence for a sequential decay through an intermediate

state in 23O. Neither a di-neutron nor phase-space model were able to describe the observed

correlations. This measurement constitutes the first observation of a two-neutron sequential

decay through three-body energy and angular correlations, and provides valuable insight

into few-body physics at the neutron dripline.

ACKNOWLEDGMENTS

During my time at MSU, I received a tremendous amount of support from my advisor, the

MoNA group, the NSCL staff, and my fellow graduate students. Without them, I could not

have completed my degree. First and foremost, I would like to thank my advisor, Michael

Theonnessen, for his wisdom, guidance, and mentorship. He was always there to answer my

questions and discuss ideas. It has been a great opportunity and a pleasure to work with

him. I also thank the other members of my committee, Remco Zegers, Alex Brown, Norman

Birge, and Phillip Duxbury for their time, advice, and guidance during our meetings.

Working with the MoNA Collaboration has been a tremendously joyful experience. The

entire collaboration has been incredibly supportive and receptive to my questions since the

day I joined. I always looked forward to the yearly meeting and will certainly miss it. Many

thanks to Nathan Frank, Paul DeYoung, and Thomas Baumann for helping with everything

from simple calibration questions to fixing the DAQ in the middle of the night, to discussing

and assisting in the analysis of our data.

I would also like to thank the other graduate students and members of the local group:

Greg Christian, Shea Mosby, Jenna Smith, Jesse Snyder, Krystin Stiefel, Zach Kohley, An-

thony Kuchera, and Artemis Spyrou for all their help and support. They, and many others,

provided insightful and valuable discussions that made these past few years productive and

very enjoyable.

The Liquid Hydrogen Target was critical to the success of this experiment and I would

like to thank Remco Zegers, Andy Thulin, and Jorge Pereira, as well as Paul Zeller, for their

support and assistance in installing and operating the target. Without their support, the

support of the MoNA Collaboration, and the staff of the Coupled Cyclotron Facility as well

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as the A1900 group, the experiment in this work would not have been a success.

Many thanks to Mike Bennet, Vincent Bader, Daniel Winklehner, Dan Alt, and Eric

Deleeuw – my office-mates and fellow members of the Technical Institute of Procrastination

in the Physical Sciences (TIPPS). Friday evening won’t be the same without the blaring

dubstep of Muse and nerf-gun fights. I would like to thank the trio of Chrises: Chris Morse,

Chris Sulivan, and Chris Prokop, for putting up with my stupid questions. I would also

like to thank Sam Lipschutz for being an outstanding Rockport salesman, and Kenneth

Whitmore for never being wrong.

I would like thank my family for their continuous loving support, and in particular, my

grandfather, who sparked my interest in physics at an early age.

Finally, I am grateful for the opportunity to work with the great faculty, staff, post-docs,

and graduate students of the NSCL, without whom this work would not have been possible.

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TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Chart of the Nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Shell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Islands of Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.2 Tensor Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Three-body Correlations and Decays . . . . . . . . . . . . . . . . . . . . . . 101.3.1 Two-Proton Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.2 Two-Neutron Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.3 Transition from 3-body to 2-body . . . . . . . . . . . . . . . . . . . . 161.3.4 Previous Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Chapter 2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . 222.1 One Neutron Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.1.1 R-Matrix deriviation . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Two Neutron Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.1 Phase space decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2.2 Sequential decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.3 Di-neutron decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Chapter 3 Experimental Technique . . . . . . . . . . . . . . . . . . . . . . . . 383.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2 Beam Production (K500, K1200) . . . . . . . . . . . . . . . . . . . . . . . . 403.3 A1900 & Target Scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 Liquid Deuterium (LD2) Target . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4.1 Target Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4.2 Temperature Control System . . . . . . . . . . . . . . . . . . . . . . 453.4.3 Gas Handling System . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4.4 Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.5 Sweeper Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.6 Charged Particle Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.6.1 CRDCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6.2 Ion Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.6.3 Timing Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.6.4 Hodoscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.7 MoNA LISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

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3.8 Electronics and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.9 Invariant Mass Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.10 Jacobi Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Chapter 4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Calibrations and Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.1.1 Charged Particle Detectors . . . . . . . . . . . . . . . . . . . . . . . . 654.1.1.1 CRDCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1.1.2 Ion Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . 724.1.1.3 Thin Scintillator . . . . . . . . . . . . . . . . . . . . . . . . 784.1.1.4 Target and A1900 Timing Scintillator . . . . . . . . . . . . 844.1.1.5 Hodoscope . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.1.2 LD2 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.1.3 MoNA-LISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.1.3.1 Charge Calibration (QDC) . . . . . . . . . . . . . . . . . . . 964.1.3.2 Position Calibration (TDC) . . . . . . . . . . . . . . . . . . 984.1.3.3 Time calibration (tmean + global) . . . . . . . . . . . . . . 99

4.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.2.1 Beam Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.2.2 Event Quality Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.2.3 Element and Isotope Identification . . . . . . . . . . . . . . . . . . . 1054.2.4 Neutron Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.2.4.1 Two-Neutron Selection . . . . . . . . . . . . . . . . . . . . . 1154.3 Inverse Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.3.1 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.3.1.1 22O + 1n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.3.1.2 21N + 1n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214.3.1.3 23O + 1n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.3.1.4 18C + 1n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.4 Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244.4.1 Incoming Beam Parameters . . . . . . . . . . . . . . . . . . . . . . . 1254.4.2 Reaction Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.4.2.1 1n Knockout, Verification 22O . . . . . . . . . . . . . . . . . 1284.4.2.2 1p Knockout, Verification 22N . . . . . . . . . . . . . . . . . 1304.4.2.3 (d,d’), Inelastic Excitation . . . . . . . . . . . . . . . . . . . 131

4.4.3 Neutron Interaction and MENATE R . . . . . . . . . . . . . . . . . . 1334.4.4 Other Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.4.5 Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.4.6 Decay Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.4.6.1 One neutron decays . . . . . . . . . . . . . . . . . . . . . . 1354.4.6.2 Two neutron decays . . . . . . . . . . . . . . . . . . . . . . 136

4.4.7 Fitting and Likelihood Ratio . . . . . . . . . . . . . . . . . . . . . . . 138

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Chapter 5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 1405.1 22O + 2n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1405.2 22N + 1n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5.2.1 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2.1.1 Ground State Decay . . . . . . . . . . . . . . . . . . . . . . 1585.2.1.2 Single State . . . . . . . . . . . . . . . . . . . . . . . . . . . 1595.2.1.3 Two State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.2.1.4 Background Discussion - Search for 24N . . . . . . . . . . . 162

5.2.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Chapter 6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 165

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

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LIST OF TABLES

Table 3.1: Boiling and triple points of hydrogen, deuterium, and neon. . . . . . 43

Table 3.2: List of components in the gas handling system. Table adopted fromRef. [89]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Table 4.1: Bad pads in the CRDCs which are removed from analysis. . . . . . . 66

Table 4.2: Slopes and offsets for the CRDC calibration. . . . . . . . . . . . . . 70

Table 4.3: Drift correction parameters for the Ion Chamber. . . . . . . . . . . . 78

Table 4.4: Coefficients for position correction (left) and drift correction (right)of the Thin scintillator. . . . . . . . . . . . . . . . . . . . . . . . . . 81

Table 4.5: Time offsets for the Thin scintillator. . . . . . . . . . . . . . . . . . 83

Table 4.6: Timing offsets for the Target and A1900 Scintillators. . . . . . . . . 85

Table 4.7: Global tmean offset in nanoseconds for each table in MoNA-LISA. . 101

Table 4.8: Time-of-flight correction coefficients for isotope separation. . . . . . 110

Table 4.9: Simulation parameters for the incoming beam distribution. Deter-mined by matching unreacted 24O in the focal plane. . . . . . . . . 127

Table 4.10: Parallel and perpendicular glauber kicks used to reproduce the CRDCdistributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Table 5.1: Error budget for the three-body decay energy. The dominant contri-bution is the drift length, dL. . . . . . . . . . . . . . . . . . . . . . . 147

Table 5.2: Spectroscopic overlaps for various states in 23N with the ground stateof 24O. Edecay is calculated assuming the state decays directly to the

ground state of 22N. . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Table 5.3: Ratio of intensities in the single state interpretation compared tothe equivalent ratio formed from spectroscopic overlaps for possibleinitial states in 23N with final states in 22N using the WBP and WBTinteractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

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Table 5.4: Spectroscopic overlaps for possible initial states in 23N with finalstates in 22N using the WBP and WBT interactions. For comparisonare the intensities for the best-fits of the data. . . . . . . . . . . . . 161

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LIST OF FIGURES

Figure 1.1: Chart of the Nuclides. On the color axis is the neutron separationenergy Sn in MeV. Data taken from AME2012 [8] . . . . . . . . . . 3

Figure 1.2: (Top) Difference in binding energy between the liquid drop model andexperimental observation. On the left is the difference as a functionof neutron number N . On the right is as a function of the protonnumber Z. (Bottom) Electron Ionization energy for all elements withZ < 104 on the periodic table. Note the similarity in closed electronshells and closed neutron/proton shells. Image sources: [10], [11] . . 5

Figure 1.3: Single particle orbits in the nuclear shell model. Energies are shownfor a harmonic oscillator potential, woods-saxon, and woods-saxonwith spin orbit. Image Source: [10] . . . . . . . . . . . . . . . . . . 6

Figure 1.4: (a) Diagram for wave function of relative motion for collision of a“spin-flip” pair. Note that this case is deuteron-like and attractive.(b) In the non spin-flip case the wave function of relative motion isstretched perpendicular to the spin (denoted by black arrows), andis repulsive. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Figure 1.5: Schematic for illustrating shell evolution due to the tensor force. Thewidth of the arrows denotes the strength of the interaction. (Left)A configuration in nuclei near stability with N = 20 being magic.(Right) As protons are removed the attraction with the ν0d3/2 orbitalweakens causing it to rise in energy relative to the ν1s1/2 orbitalcreating a new shell gap at N = 16 . . . . . . . . . . . . . . . . . . 10

Figure 1.6: (Top) Theoretical prediction for the Jacobi T (left) and Y (right)system relative energy and angular correlations in the breakup of6Be based on a full three-body calculation[44] The data are shown onthe bottom panels. Image Source: [43] . . . . . . . . . . . . . . . . . 13

Figure 1.7: Jacobi relative energy correlations in the T system for the unboundsystems (Left) 5H [51], (Right) 13Li, and 16Be [60]. Peaks at lowEx/ET indicate that the neutron-neutron energy is low relative tothe total three-body energy and is interpreted as either a di-neutronemission or final state interaction. . . . . . . . . . . . . . . . . . . . 15

x

Figure 1.8: (Top) Level structure for the three-body decay of 6Be [67]. (Bot-tom) Relative energy plots in the Jacobi Y system (proton-core) fordifferent slices in the total three-body energy. On the left, the en-ergy region is slightly above the 2+ state and the correlation indicatea three-body decay. On the right, the energy is much greater thanthe intermediate state and correlations indicating sequential emissionbegin to emerge [43] . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Figure 1.9: (Top) The transition from the three-body to the two-body regime asstudied within Grigorenko’s model for 12O and 19Mg. Plotted arethe relative energies in the Jacobi Y system [2] . (Bottom) Levelstructure for the decays of 12O [27] and 19Mg. [29]. Note the widthsof the intermediate states. . . . . . . . . . . . . . . . . . . . . . . . 19

Figure 1.10: Level structure of the most neutron rich bound oxygen isotopes.Hatched areas indicate approximate widths. . . . . . . . . . . . . . . 21

Figure 2.1: (Left) Schematic for phase-space breakup. (Right) A hypotheticallevel scheme where one would expect to observe a phase-space decay.EI denotes the three-body energy, EV the intermediate state, andEF = 0, the final state. The hatched areas indicate widths. Notethat the intermediate state is broad. . . . . . . . . . . . . . . . . . . 28

Figure 2.2: (Top) Schematic for a sequential decay. (Bottom) A hypotheticallevel scheme where one would expect to observe a sequential decay.The hatched areas indicate widths. Note that the intermediate stateis narrow and well separated from E1. . . . . . . . . . . . . . . . . . 31

Figure 2.3: (Left) Schematic for dineutron emission. (Right) A hypothetical levelscheme where one would expect to observe a dineutron. The hatchedareas indicate widths. . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 3.1: Layout of the detectors in the N2 Vault. . . . . . . . . . . . . . . . . 39

Figure 3.2: Beam production at the Coupled Cyclotron Facility [84]. 48Ca isheated up in an ion-source and accelerated by the K500 and K1200cyclotrons. After impinging on a Be target, the fragments are filteredby the A1900 to provide the desired beam. . . . . . . . . . . . . . . 40

Figure 3.3: Schematic of the Ursinus College Liquid Hydrogen Target. (Left) Ahead on view along the beam axis. (Right) Side view. . . . . . . . . 42

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Figure 3.4: Phase diagram for deuterium. The solid line marks the liquid/solidtransition, while the blue dotted line denotes the liquid/gas transi-tion. The plus marks are data obtained during the initial filling ofthe target. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 3.5: (Left) Photo of the target cell used to contain the Liquid Deuterium.The liquid drips down through the center hole seen on the targetflange. The iridium seal can be seen surrounding it before beingpressed. (Right) Drawing of the inner ring where the Kapton foil isglued. The ring is then clamped to the target by an outer ring visiblein the left photo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 3.6: A diagram of the gas handling system used to control the flow ofdeuterium in and out of the target cell. Figure adopted from [89] . . 48

Figure 3.7: Schematic of a Cathode Readout Drift Chamber (CRDC) where thez-direction has been expanded. The field shaping wires are not drawnfor visibility. Note that the electron avalance is does not begin untilthe electrons encounter the Frisch grid. . . . . . . . . . . . . . . . . 50

Figure 3.8: (Left) Head-on view (looking into the beam) of the thin timing scintil-lator. (Right) An example level scheme for transitions in the organicmaterial with a π-electron structure. Source: [91] . . . . . . . . . . . 52

Figure 3.9: Emission spectrum for EJ-204. The peak wavelength is around 410nm [92]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 3.10: Schematic of the Hodoscope, which is an array of CsI(Na) crystalsarranged in a 5x5 configuration. . . . . . . . . . . . . . . . . . . . . 54

Figure 3.11: 12C(n,*) cross sections for neutron energies ranging from 1 - 100 MeVfor several different reactions. Each of the cross sections listed hereare included in MENATE R and used to model the neutron interac-tions in MoNA-LISA. Image source: [93] . . . . . . . . . . . . . . . 56

Figure 3.12: Schematic of the electronics for MoNA-LISA and the Sweeper. Dashedlines encompases each subsystem. Green arrows indicate start signals,red stop signals, and blue arrows indicate the QDC/ADC gate for in-tegration. Upon receiving the system trigger from level 3, all TDCs,QDCs, and ADCs read out and are processed. . . . . . . . . . . . . 59

Figure 3.13: Jacobi T and Y coordinates for the three-body system 22O + 2n. . 62

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Figure 3.14: Simulated Jacobi T and Y coordinates for the three-body system 22O+ 2n with ET = 750 keV. Effects from neutron scattering have beenremoved. Acceptances and efficiencies are applied. The different col-ors indicate different decay mechanisms. All spectra are normalizedto 2 ∗ 106 events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Figure 4.1: Pedestal subtraction in the CRDCs. The raw pads for CRDC1 (left)and CRDC2 (right) are shown in the first and second panels from theleft, while the subtraction is shown in the third and fourth panels. . 67

Figure 4.2: Before (left) and after (right) gainmatching of CRDC1 and CRDC2.CRDC1 is shown in the first and third panel, and CRDC2 in thesecond and fourth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Figure 4.3: (From left to right) Mask runs 3023, 3078, and 3142 for CRDC2.Particles that illuminate an area above the mask indicate that themask did not fully insert. . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 4.4: Drift correction for CRDC1 Y position. (Top left), Uncorrected Ydistribution in CRDC1 as a function of Run Number. (Top right),Uncorrected centroids of CRDC1 Y position as a function of RunNumber. (Bottom left). Corrected Y distribution in CRDC1. (Bot-tom right) Centroids of corrected Y distribution in CRDC1 as a func-tion of run number. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Figure 4.5: Drift correction for CRDC2 Y position. (Top left), Uncorrected Ydistribution in CRDC2 as a function of Run Number. (Top right),Uncorrected centroids of CRDC2 Y position as a function of RunNumber. (Bottom left). Corrected Y distribution in CRDC2. (Bot-tom right) Centroids of corrected Y distribution in CRDC2 as a func-tion of run number. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Figure 4.6: Example of gaussian fitting procedure for gainmatching of the ICpads. Pad 4 is shown on the left, and the reference pad, pad 9 on theright. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 4.7: Results of applying the gainmatching calibration for the IC. Raw padson shown on the left and calibrated pads on the right. . . . . . . . . 75

Figure 4.8: Example of position correction in the ion chamber for pad 15. Theraw signal as a function of X position is shown in the left panel, withthe best-fit super-imposed. The right panel shows the result of thecorrection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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Figure 4.9: Drift correction for IC sum. (Top left), Uncorrected charge distri-bution in the IC as a function of Run Number. (Top right), Un-corrected centroids of the charge distribution as a function of RunNumber. (Bottom left). Drift Corrected charge distribution in theIC. (Bottom right) Centroids of the drift corrected charge distribution. 77

Figure 4.10: Before (left) and after (right) the gainmatching of the PMTs in thethin scintillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Figure 4.11: Correction of the position dependence in the thin scintillator. (Left)the raw charge signal as a function of X position with the best-fitsuperimposed. (Right) Result of position correction. . . . . . . . . . 80

Figure 4.12: Drift correction for charge collection in the thin scintillator. (Topleft), Uncorrected charge distribution in the thin as a function of RunNumber. (Top right), Uncorrected centroids of the charge distribu-tion as a function of Run Number. (Bottom left). Drift Correctedcharge distribution in the thin. (Bottom right) Centroids of the driftcorrected charge distribution. . . . . . . . . . . . . . . . . . . . . . . 82

Figure 4.13: Drift correction for the timing of the thin scintillator. (Top-left)The average time tthin is shown as a function of run number. (Top-right) The centroid of the timing signal as a function of run number.(Bottom-left) Drift corrected thin timing as a function of run number.(Bottom-right) Corrected timing centroids using the offset method. 84

Figure 4.14: Drift correction for the timing of the target scintillator. (Top-left)The timing signal is shown as a function of run number. (Top-right) The centroid of the timing signal as a function of run number.(Bottom-left) Drift corrected target scintillator timing as a functionof run number. (Bottom-right) Corrected timing centroids using theoffset method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Figure 4.15: Drift correction for the timing of the A1900 scintillator. (Top-left)The timing signal is shown as a function of run number. (Top-right) The centroid of the timing signal as a function of run num-ber. (Bottom-left) Drift corrected A1900 timing as a function of runnumber. (Bottom-right) Corrected timing centroids using the offsetmethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Figure 4.16: Light collection in the middle row of the Hodoscope for Run 3002where an 20O beam was swept across the focal plane. Ideal behaviourwould be a uniform response. On the X and Y axis are the X andY positions relative to each crystal, the color axis is the total energydeposited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

xiv

Figure 4.17: Temperature and Pressure calibration of the LD2 target. (Left) Rawvoltages from the EPICS readout from the temperature controllerand manometer. The data are in black, the region used to fit thephase transition is highlighted in red. (Right) Calibration to phase-transition (blue line) in deuterium. . . . . . . . . . . . . . . . . . . . 91

Figure 4.18: Measured phase transition with a neon test gas using the calibra-tion parameters from fitting the deuterium transition. The red linecorresponds to data from Ref [100], and the dashed lines are the un-certainty bands given a ±0.5K fluctuation. The red arrows indicatedata taken during initial cooling, liquefaction, and warming of thetarget. The events around 26 K and 1200 Torr are a result of asensor error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Figure 4.19: Temperature and Pressure fluctuations over the course of the exper-iment starting from 4:00 AM 3/19/14. Time is measured in hours. . 93

Figure 4.20: Measured kinetic energy of the 24O beam after passing through thefull LD2 target. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Figure 4.21: A 3.4 mm bulge in the LD2 drawn to scale. . . . . . . . . . . . . . . 95

Figure 4.22: Example spectra used for QDC calibration in MoNA-LISA. (Left.)Raw QDC channels for data taken with cosmic rays. The red curveis a gaussian fit to the cosmic-ray peak. (Right) Pedestal subtractedand calibrated charge spectrum. The cosmic ray peak appears around20-30 MeVee. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure 4.23: TDC and X-position calibration spectra. (Left) Raw TDC channelsfor a run taken with a time calibrator with a fixed interval of 40ns, this determines the TDC slope. (Middle) Raw time-differencespectrum used to calculate the X-position. The red lines indicate thephysical ends of the bar. (Right) Conversion of time-difference intoX-position. Data taken with cosmics which fully illuminate the array. 98

Figure 4.24: Schematic of a cosmic ray tracks used to determine the relative offsetsbetween each bar. Offsets within a table are with respect to thebottom bar in the front layer. J0 and K15 are example bars in thefirst and second layer of LISA. . . . . . . . . . . . . . . . . . . . . . 100

Figure 4.25: Reconstructed velocity of γ-rays coming from the target in coinci-dence with 22O fragments. The global timing offset is varied for eachtable to align the centroids at v = 29.97 cm/ns. . . . . . . . . . . . . 101

xv

Figure 4.26: (Left) Separation of the 24O beam by time-of-flight from the otherbeam contaminates. (Right) Energy loss vs. time-of-flight spectrumfor all beams and reaction products. Lines are drawn to guide theeye for each element. . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure 4.27: σ vs. total integrated charge in the CRDCs. Quality gates are drawnin red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Figure 4.28: Total integrated charge of CRDC1 (Y-axis) vs. CRDC2 (X-axis). Agate, shown in red, is drawn around events that deposite a similarcharge in both detectors. A gate is applied to select the 24O beam. . 104

Figure 4.29: dE vs. ToF for reaction products coming from the 24O beam. Coin-cidence with a neutron is not required. . . . . . . . . . . . . . . . . 106

Figure 4.30: 3D correlations for dispersive position, angle, and time-of-flight show-ing isotope separation for the carbon isotopes. . . . . . . . . . . . . 107

Figure 4.31: Projection of Fig. 4.30 onto the 2D plane of ToF vs. dispersiveposition for the oxygen isotopes. The contour of iso-time-of-flight isshown in black. This correlation, when plotted against the time-of-flight shows separation for the oxygen isotopes (Right), and can berotated in this plane for the purposes of making a 1D gate. . . . . . 109

Figure 4.32: Matrix of A2 vs. A/Z with the condition that Z ≤ A up to mass∼ 25. Each point is a separate nucleus (some unphysical).The redlines indicate curves of constant Z. . . . . . . . . . . . . . . . . . . 111

Figure 4.33: Energy loss dE in the ion chamber vs. Corrected time-of-flight show-ing isotope separation. A coincidence gate with a neutron is re-quired to reduced background from unreacted beam. A vertical lineat A/Z = 3 is drawn to guide the eye. . . . . . . . . . . . . . . . . . 111

Figure 4.34: One-dimensional particle identification for the Oxygen isotopes. Agate is drawn at the vertical line to select 22O. Neutron coincidencewith MoNA-LISA is required to reduce the background from unre-acted beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure 4.35: One-dimensional particle identification for the Nitrogen isotopes. Agate is drawn at the vertical line to select 22N. Neutron coincidencewith MoNA-LISA is required to identify candidates for reconstruction.112

xvi

Figure 4.36: Neutron time-of-flight spectrum in MoNA-LISA with 22O coincidence.The splitting is due to the narrow resonance in 23O and the fact thatthe MoNA-LISA tables are physically separated. The insert showsγ-rays coming from the target. . . . . . . . . . . . . . . . . . . . . . 114

Figure 4.37: Neutron time-of-flight spectrum vs. Charge deposited in MoNA-LISAwith 22O coincidence. γ-rays typically deposits < 5 MeVee, while realneutrons can deposit up to the beam energy. No background fromcosmic rays is evident. . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Figure 4.38: Relative distance D12 and velocity V12 for 1n (Left) and 2n (Right)simulations. The selection for 2n events is shown in by the shadedblue region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Figure 4.39: Comparison of neutron (blue) and fragment (black) kinetic energy forthe decay of 23O. The relative velocity is shown on the right. . . . . 120

Figure 4.40: Comparison of neutron (blue) and fragment (black) angles at thetarget. The large binning in θTY is due to the discretization of theMoNA bars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Figure 4.41: Comparison of measured neutron-fragment opening angle θn−f and

fragment angle in spherical coordinates for the decay of 23O→22O +1n. In black is the current experiment, shown in blue is a measure-ment of the same decay using the same experimental apparatus [73]for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Figure 4.42: 1n Edecay spectra for the decay of 23O. (Left) spectrum obtained fromthe current experiment. (Right) A previous measurement performedon the same experimental apparatus for comparison from Ref. [72] . 121

Figure 4.43: Edecay spectrum for the decay of 22N→ 21N + 1n. On the left is thespectrum obtained from the current experiment. (Right) A previousmeasurement of the same resonance also performed with MoNA [110]. 122

Figure 4.44: Edecay spectrum for the decay of 24O → 23O + 1n. (Left) spectrumobtained from the current experiment. (Right) A previous measure-ment of the same resonances using MoNA for comparison. [111] . . . 123

Figure 4.45: (Top) Edecay spectrum for the decay of 19C → 18C + 1n obtainedfrom the current experiment. (Bottom) A previous measurement ofthe same resonance using MoNA [112, 113]. . . . . . . . . . . . . . . 123

xvii

Figure 4.46: Comparison between simulation (blue) and data (black) for the un-reacted 24O beam in the focal plane. . . . . . . . . . . . . . . . . . 128

Figure 4.47: Reconstructed angles and target position using a 4-parameter map.The simulation (blue) is compared to data for the unreacted 24Obeam (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Figure 4.48: Comparison of reconstructed kinetic energy distributions betweensimulation (blue) and data (black) for the unreacted 24O beam. Thereconstructed energy is after passing through the full LD2 target. . . 129

Figure 4.49: Comparison of focal plane position and angles between simulation(blue) and data (black) for 1n knockout to 23O, which then decaysto 22O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Figure 4.50: Reconstructed kinetic energy for the 22O fragments coming from the1n knockout reaction. Simulation results are shown in blue and thedata in black. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Figure 4.51: Comparison of focal plane position and angles between simulation(blue) and data (black) for 1p knockout to 23N, which then decaysto 22N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Figure 4.52: Reconstructed kinetic energy for the 22N fragments coming from theproton knockout reaction. Simulation is in blue and data are in black. 133

Figure 4.53: Center of mass angular distribution for inelastic scattering of 24O ond at 82.5 MeV/u (lab), estimated with FRESCO, a global opticalmodel, and the deformation length of 12C. . . . . . . . . . . . . . . 133

Figure 4.54: Breakdown of 12C(n,*) cross-section in MENATE R. (Left.) MENATE Rcross sections without any adjustment. The blue curve is the sum ofall cross-section in the energy range 40 - 100 MeV. (Right) The totalMENATE R cross-sections after modification compared to the DelGuerra compilation [122] and the ENDF [123] evaluation. . . . . . . 134

Figure 4.55: CRDC1 X vs. CRDC1 θX for all 22O fragments coincident with aneutron. A gate, called an XTX cut, is drawn around the data andapplied to simulation. This is to reject fragments which may have astrange emittance in the simulation. . . . . . . . . . . . . . . . . . . 136

Figure 5.1: (Left) Acceptance of MoNA-LISA for a 1n decay as a function ofEdecay. (Right) Acceptance for a 2n decay with causality cuts applied.141

xviii

Figure 5.2: (a) 1n decay energy spectra for 23O with contributions from neutron-knockout and inelastic excitation. (b) The three-body decay energyfor 22O + 2n for all multiplicities ≥ 2. (c) The three-body decayenergy with causality cuts applied. The inserts show a logarithmicview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Figure 5.3: Jacobi relative energy and angle spectra in the T and Y systems forthe decay of 24O→ 22O + 2n with the causality cuts applied and therequirement that Edecay < 4 MeV. . . . . . . . . . . . . . . . . . . . 144

Figure 5.4: Level scheme for the population of unbound states in 23O and 24Ofrom neutron-knockout and inelastic excitation. Hatched areas indi-cate approximate widths. . . . . . . . . . . . . . . . . . . . . . . . . 145

Figure 5.5: (a) 1n decay energy spectra for 23O with contributions from neutron-knockout and inelastic excitation. (b) The three-body decay energyfor 22O + 2n for all multiplicities ≥ 2. (c) The three-body decayenergy with causality cuts applied. Direct population of the 5/2+

state and 3/2+ state in 23O are shown in dashed-red and dashed-green respectively. The 2n component coming from the sequentialdecay of 24O is shown in dashed-blue and decays through the 5/2+

state. The sum of all components is shown in black. The inserts showa logarithmic view. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

Figure 5.6: Jacobi relative energy and angle spectra in the T system for the decayof 24O → 22O + 2n with the causality cuts applied and the require-ment that Edecay < 4 MeV. Shown for comparison are simulations ofseveral three-body decay modes. A sequential decay (b), a di-neutrondecay with a = −18.7 fm (c), and (d) a phase-space decay. The am-plitudes are set by twice the integral of the three-body spectrum withcausality cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Figure 5.7: Neutron configurations for the two-neutron sequential decay. Filledcircle represent particles and faded circles represent holes. The 2+ or4+ configuration of 24O is shown on the far right and is a particle-hole excitation. The 5/2+ state in 23O is a hole state which decaysto the two-particle two-hole configuration of 22O which is a smallcomponent of the ground state wavefunction. . . . . . . . . . . . . 151

Figure 5.8: Comparison of experimentally measured states in 24O with USDBshell model predictions. Data taken from Refs. [70, 71]. The stateobserved in the present work is shown in blue. . . . . . . . . . . . . 152

xix

Figure 5.9: Jacobi relative energy and angle spectra in the T and Y systemsfor the decay of 24O → 22O + 2n with the causality cuts appliedand the requirement that Edecay < 4 MeV. In dashed-blue is the

sequential decay through the 5/2+ state in 23O. The remaining false2n components from the 1n decay of 23O are shown in shaded-grey.The sum of both components is shown in solid-black . . . . . . . . . 153

Figure 5.10: Two-body decay energy for 22N + 1n. . . . . . . . . . . . . . . . . . 154

Figure 5.11: Shell model predictions for 23N with the WBP and WBT Hamiltoni-ans as well as the Continuum Shell Model. . . . . . . . . . . . . . . 155

Figure 5.12: Possible level schemes that could give rise to the observed two-bodydecay energy for 23N. Case (a) is the “Ground State Decay,” whilethe “Two State” scenario is case (b), and the “Single State” case (e).The single state interpretation could also be two states close together.Cases (c), (d), and (f) are excluded due to the weak intensity of the100 keV transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Figure 5.13: Best fit of the two-body decay energy for 23N based on the “GroundState Decay” interpretation. The purple curve indicates the 100 keVtransition, the dahsed red is the 960 keV transition. The 2n back-ground is shown in shaded gray. . . . . . . . . . . . . . . . . . . . . 158

Figure 5.14: Best fit of the two-body decay energy for 23N based on the “SingleState” interpretation. The purple curve indicates the 100 keV transi-tion, the dahsed red is the 960 keV transition, and the dashed blue isthe 1100 keV transition. The 2n background is shown in shaded gray. 160

Figure 5.15: Best fit of the two-body decay energy for 23N based on the “TwoState” interpretation. The purple curve indicates the 100 keV transi-tion, the dahsed red is the 960 keV transition, and the dashed blue isthe 1100 keV transition. The 2n background is shown in shaded gray. 162

Figure 5.16: Comparison between a 1n thermal background (Top) and a 2n back-ground (Bottom). On the left is the two-body decay energy. Themiddle panels shown the three-body spectrum for 24N with causalitycuts, and the far right panels show the multiplicity. The purple lineis the E1 = 100 keV Breit-Wigner, the dashed red is the E2 = 960keV resonance. The background contribution is shown in shaded gray. 163

xx

Chapter 1

Introduction

1.1 Chart of the Nuclides

The atomic nucleus consists of two types of composite particles with similar mass: protons

and neutrons. Protons carry one unit of positive charge e and neutrons are charge-neutral.

A nuclear species is characterized by the number of protons it contains, Z, and a mass

number A so defined such that the mass of a single nucleon is nearly one. In the nucleus

we encounter length scales on the order of 10−15m, densities on the order of ∼ 2.3 ∗ 1017

kg/m3, and energies typically in the keV to MeV range. The time-scales for nuclear processes

vary over an enormous range. β and α decay can take place on the order of milliseconds to

hours, or even thousands or millions of years. Electromagnetic decays typically occur within

lifetimes of 10−15s, and the breakup of particle-unbound resonances, like 25O, are extremely

short – occurring on timescales of 10−21s [1, 2].

Similar to the periodic table, which arranges elements, the chart of nuclides arranges

all known nuclear species by the number of protons (Y -axis), and number of neutrons

(X-axis), shown in Fig. 1.1. For example, plotting the neutron separation energy Sn, the

energy required to remove a single neutron, immediately reveals a global trend evidenced

by a staggering pattern in Fig. 1.1. This even-odd oscillation between separation energies

can be explained by two-body pairing (n − n) which can increase/decrease the binding.

The same trend is observed for protons. The chart of nuclides at present is far from being

1

completely explored, and the limits for existence are unknown. Of the approximately 3000

known nuclei there is an estimated 4000 more that may exist [3]. The proton dripline is

unknown for the heaviest elements and the neutron dripline is only known up to 24O[4].

There are also predictions for an “island of stability,” a region in the superheavies of stable

nuclei yet unobserved but expected to occur around Z = 114, N = 184 [5].

The over-arching goal of nuclear physics is to understand, with predictive power, the

interactions between neutrons and protons and the properties of the complex many-body

systems they can create when arranged together. So strictly speaking, nuclear physics is

strong interaction physics and based upon the Standard Model, we should be concerned

with gluon exchange between the constituent quarks. However the typical energy scale

characteristic of nuclear physics is in the low-energy regime of QCD where the theory is

non-perturbative, so direct calculation is difficult. Although the problem can be approached

on a discretized lattice (lattice QCD), this method is still limited by computational power

and has so far only been implemented in the lightest nuclei (3He, 4He) [6]. In addition,

in 1979, Weinberg [7] pointed out that any effective theory for nucleons and mesons that

obeys the same symmetries as QCD is equivalent to QCD, which allows us to consider

nucleons and mesons as our starting point instead of quarks. Even this reduction can be

untractable computationally. If one starts with a bare two-nucleon NN interaction, then

any nuclear many-body problem can be exactly defined, but the problem grows factorially

and these microscopic calculations are limited to only the lightest nuclei. A nucleus like 238U

is simply impossible to compute from a bare NN potential, and will likely be for some time.

At present there is no single theoretical formulation that allows us to interpret all nuclear

phenomena in a fundamental way, and so nuclear physics is approached phenomenologically.

The appropriate model depends on where one is in the nuclear chart and what phenomenon

2

is being discussed. It is from these models that we gain insight into nuclear structure.

Neutron Number0 20 40 60 80 100 120 140 160

Pro

ton

Nu

mb

er Z

0

20

40

60

80

100

120

0

2

4

6

8

10

12N = Z

[MeV]nS

Figure 1.1: Chart of the Nuclides. On the color axis is the neutron separation energy Sn inMeV. Data taken from AME2012 [8]

1.2 Shell Model

One successful model is the Shell Model. Early electron and Rutherford scattering exper-

iments showed, surprisingly, that the charge and matter radii of nuclei are nearly equal to

within about 0.1 fm [1, 9] – implying that the nuclear force is the same between neutrons

and protons. (Although not quite true as the symmetry is broken by the slight difference in

quark masses). Both have an A dependence as:

r ∼ r0A1/3

3

with r0 = 1.2 fm. From these measurements, the density profile as a function of r was

found to be largely constant within the nucleus, with a smooth fall-off as one approaches the

surface. Because of the short range of the nuclear interaction, nucleons mainly interact with

their neighbors and saturation occurs where nucleons on the surface do not interact strongly

with those in the core. This observation first lead to the liquid-drop model, proposed by

Gamov, where the nucleus was thought of like a droplet of liquid. The binding energy can

be expressed in the following way:

BE(N,Z) = α1A− α2A2/3 − α3Z2

A1/3− α4

(N − Z)2

A

Where the four terms refer to the volume, surface, Coulomb, and symmetry terms, respec-

tively. The first is a result of constant density, while the second accounts for the fact that the

nucleons on the surface have less neighbors to interact with. The third results from Coulomb

repulsion between the protons, and the fourth term can be understood as an effect of the

Pauli principle.

While a good estimator of the average binding energy, the liquid drop model does not

account for any shell or pairing effects. Similar to nobel gases, which have full electron shells,

there are certain numbers of neutrons and protons that are more tightly bound than others.

Fig. 1.2 shows the difference between the liquid drop model prediction for binding energy

and what is observed in experiment. Large peaks appear at what are called the “magic

numbers,” 28, 50, 82, 126, where one observes more binding in nature than predicted by

the liquid drop-model. This is strikingly similar to spikes in the electron ionization energy

occurring in the nobel gasses. Thus inspired by the atomic shell model, Maria Goppert

Mayer, Haxel, Jensen, and Suess all sought to explain the enhanced binding with a similar

4

Figure 1.2: (Top) Difference in binding energy between the liquid drop model and experi-mental observation. On the left is the difference as a function of neutron number N . On theright is as a function of the proton number Z. (Bottom) Electron Ionization energy for allelements with Z < 104 on the periodic table. Note the similarity in closed electron shellsand closed neutron/proton shells. Image sources: [10], [11]

approach [12, 13]. This idea is particularly attractive because now spatial orbits for nucleons

can be discussed in analogy to electron orbitals.

The first step in developing a shell model is to choose a potential. Due to the short-range

interaction and constant density, a nucleon in the middle of the nucleus will interact with

approximately the same number of nucleons regardless of it’s position. Thus the potential

5

should be flat inside the nucleus, and negative so that the nucleus is bound, V (r) < 0.

As the nucleon moves towards the surface the number of neighbors it can interact with

decreases leading to a shallower potential. Finally, outside the nucleus, we exceed the short-

interaction range, and so V (r) should approach zero. This behavior is often parameterized

with a Woods-Saxon shape, which can be further approximated by a harmonic oscillator.

By adding a spin-orbit term, Mayer and Jensen were able to reproduce the observed gaps in

orbital energy, corresponding to the magic numbers, for which they were awarded the Nobel

Prize (1963).

Figure 1.3: Single particle orbits in the nuclear shell model. Energies are shown for aharmonic oscillator potential, woods-saxon, and woods-saxon with spin orbit. Image Source:[10]

6

The nuclear shell model shares some properties with the atomic shell model. A single

particle is placed in a mean-field V (r), and the eigenstates are characterized by orbitals

with quantum numbers n, l, j, and an energy E. Like atomic orbitals, the eigenstates are

filled separately with neutrons and protons beginning with the lowest energy while obeying

the Pauli principle. However, unlike the atomic shell model, the spin-orbit term is greater

and of opposite sign, so the ordering of the orbitals and the placement of shell gaps (magic

numbers) is different.

Since Mayer and Jensen’s work, the Shell Model has become much more sophisticated.

A more modern calculation will write the Hamiltonian as a sum of one- and two-body op-

erators, with an effective two-body interaction typically derived phenomenologically from

experimental measurements in a particular mass-range of interest. The problem then be-

comes one of matrix-diagonalization to determine the eigenvalues of a particular few-body

system. It is a good simplification to assume that at the shell-closures the nucleons in a

filled shell can be approximated as a single core. This approach also has computational limi-

tations, as the number of basis states increases factorially with the addition of more orbitals

and/or particles and truncations are often made to simplify the calculation.

1.2.1 Islands of Inversion

It has been shown that Mayer and Jensen’s magic numbers break down as one moves towards

neutron rich nuclei. The conventional magic numbers for nuclei in the valley of stability are

not necessarily magic for nuclei with extreme N/Z ratios. For example 24O is doubly magic

with the appearance of a new shell closure at N = 16, as evidenced by trends in E(2+)

energies [14, 15, 16]. One striking example is the “Island of Inversion,” located around the

mass region of A ∼ 32 [17, 18]. Here, the N = 20 shell gap is quenched and nuclei that

7

should occupy ground states in the sd shell instead occupy orbitals in the pf shell. This

shift has been attributed to the NN tensor force [19], three-body forces [20], and continuum

effects in cases where nuclei approach the driplines [21]. The discovery of the island of

inversion caused a paradigm shift, as it was previously thought that the magic numbers were

immutable [20]. It has since been found that there are multiple such islands of inversion,

and the effect of nuclear forces on the shell structure of nuclei, particular in neutron-rich

regions, is an ongoing area of research.

1.2.2 Tensor Force

The tensor force is the result of one-pion exchange and is the most prominent spin-isospin

interaction between nucleons. In recent years it has been shown to have systematic effects

on the single-particle energies of exotic nuclei [19, 22]. Depending on the angular momenta

of the particles involved, the tensor force can be either attractive or repulsive. The tensor

force is written as:

VT = (~τ1 · ~τ2)S12V (r)

where ~τi denotes the isospin operators of nucleons 1 and 2, V (r) > 0 is a function of the

distance r between the nucleons, and S12 is:

S12 = 3(~s1 · r)(~s2 · r)− (~s1 · ~s2)

where ~si are the spin of the nucleons. For simplicity, take ~s1 = ~s2 = +z, and let ` and `′

denote the angular momentum of a proton and neutron respectively. Their total angular

momentum will be j± = `± 1/2, and j′± = `

′ ± 1/2.

8

For “spin-flip” partners, (j±, j′∓) the tensor force is attractive. When the nucleons collide,

they will have large relative momentum causing the spatial wavefunction to be narrowly

distributed in the direction of the collision like that illustrated in the left of Fig. 1.4.

This results in a wavefunction similar to the deuteron. In this case, ~s1 · ~s2 = +1, and

~s1 · r = ~s2 · r = 1, thus S12 = 2. Since (~τ1 · ~τ2) = 2(T 2 − 3/2) = −3 for opposite isospins,

(T = τ1 + τ2 = 0), VT becomes negative and thus the interaction is attractive.

In the opposite case with (j±, j′±), the wave function is stretched along the direction of

motion as illustrated in the right of Fig. 1.4. In this case ~si · r = 0 and we obtain S12 = −1

making the interaction repulsive.

Figure 1.4: (a) Diagram for wave function of relative motion for collision of a “spin-flip”pair. Note that this case is deuteron-like and attractive. (b) In the non spin-flip case thewave function of relative motion is stretched perpendicular to the spin (denoted by blackarrows), and is repulsive.

The role of the tensor force in driving shell evolution is illustrated in Figure 1.5. For

stable nuclei near N = Z = 20, the proton π0d5/2 orbital (j+) is full and has an attraction

with the neutrons in the ν0d3/2 orbital (j′−), as well as a repulsion with ν0f7/2 orbital (j

′+).

This results in the normal shell-ordering at stability, as the ν0f7/2 orbital is raised and the

9

ν0d3/2 orbital is lowered creating a large gap at N = 20. If one removes protons and travels

down the isotones, the π0d5/2−ν0d3/2 attraction is weakened causing the the ν0d3/2 orbital

to rise in energy relative to nuclei at stability. This creates a gap between the ν0d3/2 and

ν1s1/2 orbitals leading to a quenching of the N = 20 gap, and the appearance of a new

magic number at N = 16.

Figure 1.5: Schematic for illustrating shell evolution due to the tensor force. The widthof the arrows denotes the strength of the interaction. (Left) A configuration in nuclei nearstability with N = 20 being magic. (Right) As protons are removed the attraction with theν0d3/2 orbital weakens causing it to rise in energy relative to the ν1s1/2 orbital creating anew shell gap at N = 16

1.3 Three-body Correlations and Decays

In a three-body decay there are three particles in the final state. Nuclei which undergo 2n or

2p emission, such as 10He(2n) [23, 24, 25], 13Li(2n) [23, 26], 12O(2p)[27, 28], 19Mg(2p)[29, 30,

31]), and many others discussed in this section, fall into this category. Correlations between

the two nucleons as well as the heavy core can provide insight into the decay mechanism.

In general, there are several broad categories used to classify the different decay modes: (1)

Di-neutron/proton emission, (2) a sequential decay, or (3) a three-body decay wherein it

10

is necessary to solve the three-body schrodinger equation. The latter is a true three-body

processes and can be complex. It is also useful to introduce the concept of a phase-space

decay (which is distinct from a three-body interaction), where the phase volume (M2fn vs.

M2n−n) is uniformly populated. The dineutron, phase-space, and sequential decay modes are

discussed in detail in Section 2.2.

In the two-body decay, a resonance can be characterized by just an energy and a width.

The addition of a third particle however allows for 9 degrees of freedom in the final state if we

neglect spin. Three of them describe the center-of-mass motion, and another three describe

the Euler rotations that define the decay plane. Thus for a given three-body energy ET ,

there are two free parameters left. In the Jacobi coordinate systems, discussed in detail in

section 3.10, it is convenient to choose the relative energy ε and angle θk between the Jacobi

momenta. These correlations are sensitive to the decay mechanism, and can in principle be

reproduced with the three-body wavefunction. Thus they are a powerful tool to discern the

decay mechanism, as well as connect directly with few-body kinematics. Measurement of 2p

and 2n decays and their three-body correlations near the driplines provide an opportunity to

benchmark our theoretical understanding of few-body quantum mechanics as well potentially

observe new phenomena.

1.3.1 Two-Proton Decay

The first mention of true two-proton emission is in the work of Zeldovich [32], with a more

explicit and detailed description given by V.I. Goldansky soon after [33]. Although first

predicted by Goldansky in 1960, it took nearly 40 years to confirm the existence of two-

proton radioactivity in 45Fe [34], and since then many other nuclei have been found to have

lifetimes long-enough to fall into the regime of radioactivity (τ > 10−14 s) including 17Ne

11

[35], 19Mg [36], 48Ni [37], and 54Zn [38]. While a stringent limit for radioactivity does not

exist, one definition suggested by Pfutzner [2] is “A process of emission of particles by an

atomic nucleus which occurs with characteristic time (half-life) much longer than the K-shell

vacancy half-life in a carbon atom (2 ∗ 10−14 s).” Hence a nuclear process whose duration

exceeds this limit could be considered radioactive, including the decay of unbound ground

states.

Experimental attempts to search for 2p emission started in the lightest nuclei as they are

relatively easier to access experimentally, with the first systems studied being 6Be [39, 40],

12O [28, 41] and 16Ne [42].

The decay of 6Be falls into the class of “democratic decays”, where there is no strong

energy focusing of the particles and their momenta are smoothly distributed. Even in

Geesaman’s work [39] it was evident that a simple phase-space decay, di-proton decay, or

even simultaneous emission of two p-wave protons could not describe the energy distribu-

tion of α particles they observed. It was concluded that a full three-body calculation was

necessary. More recently, the full picture of the three-body correlations in 6Be was experi-

mentally measured and shown to be in very good agreement with a three-body calculation

by Grigorenko. Fig. 1.6 shows the the T and Y Jacobi correlations for the breakup of 6Be

→ p + p + α from Ref. [43], compared to the theoretical model [44]. A full three-body

approach was also shown to be necessary to understand the p− p correlations in 16Ne [30],

19Mg [30], and 45Fe [44].

In the case of 12O the opening angle between the emitted protons was measured and was

inconsistent with models for di-proton emission [28]. It was later found that the intermediate

nucleus, 11N, has a ground state below 12O. The state is broad – implying that 12O cannot be

a Goldansky-like true 2p emitter. Initial measurements interpreted the decay as sequential

12

Figure 1.6: (Top) Theoretical prediction for the Jacobi T (left) and Y (right) system rel-ative energy and angular correlations in the breakup of 6Be based on a full three-bodycalculation[44] The data are shown on the bottom panels. Image Source: [43]

[28], however more recent work has shown that 12O more appropriately falls in the category

of 6Be, as the three-body energy ET is comparable to the width of the intermediate state

[27]. A study of 14O [45] also found evidence for sequential emission, and although not a 2p

decay, there is evidence for sequential decay in the three-body exit channel of 9B→ p + 2α

which passes through an intermediate state in 5Li [46].

There are several cases of β-delayed 2p emission, further discussed by Blank and Borge

in 2008 [47]. The most studied case, 31Ar [48] appears to decay only by sequential emission,

and it is currently believed that all studied β2p processes are sequential [2].

In general, for 2p emitting nuclei, the mechanism is either a true three-body process

or sequential, although there are some cases with evidence for di-proton emission. For

13

example, the breakup of 8C → 2p+6Be→ 4p + α was measured recently at the National

Superconducting Cyclotron Laboratory [46]. In this study, it was found that this decay can

be described as two 2p decays with the first step 8C → 2p+6Be showing some di-proton

characteristics, and the second being a three-body decay. In addition, there are studies

on the 1− resonance in 18Ne populated by 17F + 1H [49] and by Coulomb excitation [50]

where the p− p correlation spectra are explained with a di-proton component. However the

statistical claims in both cases are weak.

1.3.2 Two-Neutron Decay

Compared to 2p decays along the proton dripline, the neutron dripline is less studied. Analo-

gous to the 2p emitters, several two-neutron unbound systems have been measured including

5H [51], 10He [52, 25, 23, 24], 13Li [23, 26], 14Be [53], 16Be [54], and 26O [55, 56]. Several

of the three-body correlations in these system have been interpreted as di-neutron emission

[26, 54]. In addition, 26O has potential to exhibit two-neutron radioactivity [57]. Despite

observing 2p radioactivity approximately a decade ago, up until recently there has been “no

theoretical treatise” (Grigorenko, 2011) [58] for neutron radioactivity. This is partly due to

the fact that neutron radioactivity is yet unobserved, but also that 2n unbound systems are

challenging from both an experimental and theoretical point of view. The Coulomb interac-

tion plays a major role in understanding the dynamics of 2p emission, especially in heavier

systems like 45Fe, and extending these models to the neutron drip line is not as simple as re-

moving Coulomb effects [59]. In addition, it is difficult to identify two independent neutrons

within a single event experimentally.

Contrary to the 2p decays, many of the three-body correlations in 2n emitters indicate

di-neutron emission, or a strong n−n final state interaction (FSI). Fig. 1.7 shows the relative

14

n−n energy, Ex compared to the total three-body energy ET in the Jacobi T system for 5H

[51], 13Li [26], and 16Be [60]. All three spectra are similar and peak at low n−n energy which

can be interpreted as the wavefunction having a di-neutron component, or n−n FSI effects.

Correlations for 26O have also been measured and potentially show di-neutron like character

as well [61]. However, in this case the statics are low and the data are indistinguishable from

a model where the neutrons are emitted back-to-back rather than a cluster [62]. In these

nuclei, the intermediate nucleus is energetically inaccessible and the level structure mimics

a “Goldansky true 2p” emitter illustrated in Fig.2.3.

Figure 1.7: Jacobi relative energy correlations in the T system for the unbound systems(Left) 5H [51], (Right) 13Li, and 16Be [60]. Peaks at low Ex/ET indicate that the neutron-neutron energy is low relative to the total three-body energy and is interpreted as either adi-neutron emission or final state interaction.

Sequential correlations along the neutron drip-line have been least observed. There is a

measurement of the decay of highly excited states in 14Be [53] where the three-body energy

correlations show some evidence for decays through intermediate states. However this work

did not publish angular correlations. There is also indication that excited states in 24O can

decay by sequential emission, as evidenced by Hoffman [63] but the statistics were insufficient

to extract three-body correlations.

15

β-delayed multineutron emission, while dominant in the very neutron-rich nuclei, is not

well studied and correlations have not been measured in these systems. This is in part due to

the difficulty of neutron detection, and the fact that few cases are known. The first β-delayed

neutron decays were discovered in 1979 [64] and 1980 [65], both β2n and β3n processes were

observed in 11Li. In addition, there is a report of β4n emission in 17B [66], however this

work is unconfirmed.

1.3.3 Transition from 3-body to 2-body

The level structure of the nuclei involved in either 2p or 2n emission strongly influence,

although do not appear to completely determine, the mechanism of the decay. Just because

a sequential decay is energetically viable, does not guarantee it will occur. In the democratic

decay of 6Be the transition from three-body to sequential was examined by looking at the

p − α energy in the Jacobi Y system for different slices of the total three-body energy ET

[43]. Fig.1.8 shows the level structure of 6Be and the intermediate nucleus 5Li. Because the

intermediate state in 5Li is broad, the sequential decay mechanism is suppressed in favour

of three-body dynamics.

In this study it was found that sequential correlations were not visible until the decay

energy ET was greater than twice the intermediate state plus its width. This is shown in

Fig.1.8 by the double-hump structure in the Eα−p/ET spectrum, indicating a high-energy

and a low-energy proton coming from discrete states. Contrast this with the three-body

bell-curve at lower ET , which peaks at 1/2 and is symmetric. The symmetry is a result

of the two protons being indistinguishable, and the maximum at 1/2 can be understood

as a result of the maximum probability for barrier penetration occurring when the proton

energies are equal. Goldanksy proposed an exponential factor w(ε) as the product of two

16

Figure 1.8: (Top) Level structure for the three-body decay of 6Be [67]. (Bottom) Relativeenergy plots in the Jacobi Y system (proton-core) for different slices in the total three-bodyenergy. On the left, the energy region is slightly above the 2+ state and the correlationindicate a three-body decay. On the right, the energy is much greater than the intermediatestate and correlations indicating sequential emission begin to emerge [43]

usual barrier factors [33]:

w(ε) = exp

[−2π(Z − 2)α

√M√

ET

(1√ε

+1√

1− ε

)]

Here ET is the total three-body energy, and ε and (1-ε) the fraction of energy given to each

17

proton and α = e2/~. This expression is maximum when the two proton energies are the

same (ε = 0.5).

However, sequential correlations in 19Mg were observed in the decay of excited states once

they were energetically available because the intermediate 1− state in 18Na is narrow giving

a well defined proton energy and longer life-time [30, 29]. The transition from the three-

body to the two-body regime was examined for 12O (democratic), and 19Mg (democratic

g.s. sequential excited) within the context of a full three-body calculation [2]. Plotted in

Fig. 1.9 are the predictions for the p−core energy in the Jacobi Y system from Grigorenko’s

three-body model for 12O and 19Mg with increasing energy ET . In the case of 12O, which

is similar to 6Be, even though the energy is high enough to undergo a sequential decay a

full three-body process is favoured due to the large width of the intermediate state. This

is evidenced by the three-body bell-curve, which simply becomes narrower. In contrast, as

the energy in the 19Mg system is increased large “horns” begin to appear around 0 and 1

indicating two discrete proton energies. As the energy increases further, the horns begin to

dominate more of the spectrum. The exact limits for transitioning from a three-body decay

to a sequential decay are not known. Empirical estimates from Grigorenko’s three-body

model give the requirement:

ε0ET < E2r

Which is derived from finding the point where the probabilities from the three-body bell-

curve equal that of the sequential horns. In addition, ε0 varries between ε0 ∼ 0.3 − 0.84

depending on the life-time of the decay [2]. This is less restrictive than the original condition

18

proposed by Goldansky:

ET + Γ2r/2 < E2r

Nevertheless, if we wish to observe sequential correlations in 2n unbound nuclei, we need to

look for systems with narrow states in the intermediate nucleus.

Figure 1.9: (Top) The transition from the three-body to the two-body regime as studiedwithin Grigorenko’s model for 12O and 19Mg. Plotted are the relative energies in the JacobiY system [2] . (Bottom) Level structure for the decays of 12O [27] and 19Mg. [29]. Note thewidths of the intermediate states.

19

1.3.4 Previous Experiments

24O, the last bound isotope for which the neutron drip-line is established, is an ideal can-

didate for observing a two-neutron sequential decay. It’s structure has been well studied

as well as the intermediate nucleus 23O. There is substantial evidence for the appearance

of a new magic number N = 16 [16, 68, 15, 69], and two unbound resonances have been

observed below the two-neutron separation energy at 4.7 MeV and 5.3 MeV, with respective

spin-parity assignments 2+ and 1+ [70, 63, 71]. There is also evidence for a state above the

two-neutron separation energy S2n = 6.93 ± 0.12 MeV, at approximately 7.5 MeV [63]. In

addition, the intermediate nucleus 23O, has a low-lying narrow 5/2+ resonance at 45 keV

above the 1n separation energy [72, 73, 68]. The next excited state, a 3/2+, lies at 1.3

MeV [74]. The level structures of these nuclei are ideal to observe sequential emission and

is summarized in Fig. 1.10. The condition found in the 6Be study [43]:

E3body > 2 ∗ E2body + Γ2body

is well satisfied if the decay proceeds from the 7.5 MeV state through the 5/2+ state. First

tentative evidence that this resonances decays by sequential emission of two neutrons was

deduced from a measurement of two discrete neutron energies in coincidence similar to a

γ-ray cascade [63]. Since the three-body state is at roughly ∼ 600 keV relative to the ground

state of 22O and the intermediate state in 23O low-lying and narrow, this state is the optimum

case for observing sequential correlations. This is the goal of the current experiment, as full

three-body correlations demonstrating a sequential decay have not yet been observed on the

neutron drip-line.

20

E [MeV]

0

1

2

22O 23O 24O

0+ S2n = 6.9 MeV5/2+

45 keV

3/2+1.3 MeV

1/2+ Sn = 4.2 MeV

0+

(2+)(1+)

4.7 MeV

5.3 MeV

∼7.5 MeV

Figure 1.10: Level structure of the most neutron rich bound oxygen isotopes. Hatched areasindicate approximate widths.

21

Chapter 2

Theoretical Background

2.1 One Neutron Decay

This section gives a derivation of the energy-dependent Breit-Wigner lineshape that is used

to model an unbound resonance in the case of 1n decay using the R matrix formalism.

Models for two-neutron decays use lineshapes that depend on the decay mechanism and are

discussed in later sections.

2.1.1 R-Matrix deriviation

One-neutron unbound states can be populated in a number of ways. In this experiment

unbound states in 23N and 23O were populated via one-proton/neutron removal from an

24O beam. The resulting nuclei then proceeded to decay by emitting a neutron and a

charged fragment. This process is taken to be a direct reaction which populates the unbound

state and then promptly decays. The decay of the unbound nucleus can be interpreted as

an inelastic scattering problem in the context of R-matrix theory. However, rather than

make predictions based on the Hamiltonian, here we use R-matrix phenomenlogy to derive a

resonance lineshape that will be fit to the data based on a pole energy ep and width amplitude

γpα. Only a summary is presented here, additional details can be found in Thompson and

Nunes [75] and Lane and Thomas [76]

22

The problem we want to consider involves different entrance and exit channels as we

want to describe the unbound resonance, not just elastic scattering. In this context this

can be considered as inelasticly scattering from channel α to another α′. The method for

the multi-channel problem uses as basis states, the eigenfunctions of the real part of the

diagonal potential in each channel wα, where α denotes the channel. It can be shown that

the generalization in this case for channel α and pole p, the R matrix is: [75]

Rα′α =P∑p=1

γpαγpα′

ep − E

Where E is the incident particle energy, ep is the pole energy (resonance), and γpα are the

reduced width amplitudes. In general the γpα are constructed from an expansion of wα [75].

We wish to describe the cross section σ, which is proportional to the absolute squre of the

S matrix. In terms of the R matrix, the S matrix can be written as:

S = (t1/2H+)1− aR(H−

′/H− − β)

1− aR(H+′/H+ − β)

Where H± are diagonal matricies whose elements are the Hankel functions which are con-

structed from the regular Coulomb functions, H±l = Gl± iFl. The matrix t is diagonal with

elements tα ≡ ~2/2µα and β is the logarithmic derivative of the R matrix evalulated at the

channel radius a, which is an arbiratry cut-off point past which only long-range interactions

play a role. µα is the reduced mass. It is useful to define a “logarithmic” matrix L:

L = H+′/H+ − β =1

a(S + iP − aβ)

Where we have introduced the penetrability P and shift function S, which are diagonal

23

matrices with elements:

Pα =kαa

F 2α +G2

α(2.1)

Sα = (FαFα + GαGα)Pα (2.2)

The dot denotes a derivative with respect to ρ = kR, where k is the quantum mechanical

wavenumber, and R the radial coordinate. Since H−′/H− = L∗, the scattering matrix S

can be put in the following form:

S = Ω(tH−H+)−1/21− aRL∗

1− aRL(tH−H+)1/2Ω

Where we have introduced Ω, yet another diagonal matrix with elements Ωα = eiφα with φα

being hard-sphere phase shifts. The matrix product tH−H+ is diagonal with elements:

H−αH+α tα =

~vαa2Pα

Where v = ~k/µ is the channel velocity.

The cross section is proportional to the absolute square of the symmetric matrix S, which

is constructed from S via a similarity transformation S ≡ v1/2Sv−1/2 and can be written

as:

S = Ω[1 + 2iP 1/2(1− aRL)−1RP 1/2]Ω

Which is powerful, as we now have an expression for the S matrix from the R matrix in

24

terms of the penetrabilities and shift functions (Eqs. 2.1 and 2.2). This expression can be

greatly simplified by making several assumptions. First suppose that there are only two

channels, the elastic and inelastic resonance where the mass is partitoned differently. We

also assume that there is only one energy level in the unbound nucleus, i.e. a single pole ep.

Note that S12 = S21, we obtain in this case:

S12 = eiφ1

2iP1/2α γαγα′P

1/2α′

(ep − E)(1− aR11L1 − aR22L2)

eiφ2= eiφ1

2iP1/2α γαγα′P

1/2α′

ep − E − γ21(S1 − aβ)− iγ21P1 − γ22(S2 − aβ)− iγ22P2

eiφ2(2.3)

Define the formal width Γα:

Γα = 2γ2αPα (2.4)

As well as S0α, the energy shift ∆α, and total energy shift ∆T in addition to the total formal

width ΓT :

S0α = Sα − aβ

∆α = −γ2αS0α

∆T =∑α

∆α = −γ21S01 − γ22S02

ΓT =∑α

= 2γ21P1 + 2γ22P2

The value of −aβ can be set to any constant. Lane and Thomas [76] suggest using −aβ =

Sα(e0). Substitution of these definitions into Eq. 2.3 reduces the form of S12 considerably.

25

It already begins to take on the shape of a Breit-Wigner distribution:

S12 = eiφ1

iΓ1/21 Γ

1/22

(ep − E + ∆T ) + iΓT /2

eiφ2Recall that the cross-section is related to the symmetric S matrix by the following relation:

σαα′(E) =π

k2igJtot|Sαα′|2

Where ki is the wavenumber of the entrance channel and the spin weighting factor gJtot is:

gJtot ≡2Jtot + 1

(2Ipi + 1)(2Iti + 1)

Ji is the total spin of the populated state and Ipi , Iti are the spins of the projectile and

target-like fragments respectively. Substitution of S12 into this expression yields:

σ12 =π

kigJtot

Γ1Γ2

(E − ep + ∆T )2 + Γ2T /4

(2.5)

We are only interested in describing the decay of an unbound state. It is assumed that

the population mechanism is unimportant. Eq. 2.5 can be factored into two expressions:

σ12 =

(π

kigJtotΓ1

)(Γ2

(E − ep + ∆T )2 + Γ2T /4

)

The first describes the population of the unbound state which we are unconcerned with. We

only wish to know the E dependence of σ for the unbound state, and so this term is treated

as a constant. In addition, the probability to decay through the entrance channel is small,

26

Γ2 >> Γ1, thus ΓT ∼ Γ2 and ∆T ∼ ∆2. The lineshape for the neutron decay reduces to:

σl(E; ep,Γ0) ∝ Γl(E; ep; Γ0)[ep − E + ∆l(E; ep,Γ0)

]2+ 1

4

[Γl(E; ep,Γ0)

]2 (2.6)

Here we have dropped the subscripts for the channels and explicitly state the angular mo-

mentum dependences. Γ0, the width of the decay at ep, is used as a substitute for the partial

width γ2 (Eq. 2.4):

Γ0 = 2γ2Pl(ep)

Equation 2.6 is used to define the probability distribution for the decay energy Edecay in

simulation.

2.2 Two Neutron Decay

In two-body kinematics, the masses of the particles and the decay energy completely deter-

mine the system by conservation of energy and momentum. The addition of a third particle

increases the number of degrees of freedom and adds complexity. The energies are no longer

monochromatic, but E and P conservation still place kinematic boundaries on what mo-

menta are possible, and all three particles are emitted in the same plane. In modelling the

two-neutron decay of an unbound state three simple models are used: (1) A phase space de-

cay, (2) a di-neutron model, and (3) a sequential decay. The choice of model determines the

energy of each neutron as well as whether the decay proceeds as a true three-body breakup,

or multiple two-body processes.

27

2.2.1 Phase space decay

The phase space model assumes no correlations between the outgoing particles by uniformly

sampling the phase space of the invariant mass pairs m212 and m2

23 while applying kine-

matic constraints to conserve energy and momentum. This model is used as a baseline for

simulating the detector response for observing no three-body correlations.

P, MA A-2

p1, m1

p3, m3

p2, m2

A A− 1 A− 2

EI ,ΓI

EV ,ΓV

EF

Figure 2.1: (Left) Schematic for phase-space breakup. (Right) A hypothetical level schemewhere one would expect to observe a phase-space decay. EI denotes the three-body energy,EV the intermediate state, and EF = 0, the final state. The hatched areas indicate widths.Note that the intermediate state is broad.

Consider the decay of a particle of mass M and momentum P into three products denoted

by mi, pi, and energy Ei as illustrated in Fig. 2.1. Take c = 1, and define pij = pi + pj , and

m2ij = p2ij . Then we obtain the relations:

m212 +m2

23 +m213 = M2 +m2

1 +m22 +m2

3

And

m212 = (P − p3)2 = M2 − 2ME3 +m2

3

Where E3 is the energy of the third particle in the rest frame of M . In this frame all

particles lie within a plane and their relative orientation can be fixed if their energies are

28

known. Define the quantities:

E∗2 =(m2

12 −m21 +m2

2)

2m12

E∗3 =(M2 −m2

12 −m23)

2m12

For a given value of m212, m2

23 is maximum or minimum when p2 is parallel or anti-parallel

to p3. Setting ~p2 = ± ~p3 we obtain the limits:

(m223)max = (E∗2 + E∗3)2 −

(√E∗22 −m2

2 −√E∗23 −m2

3

)2

(m223)min = (E∗2 + E∗3)2 −

(√E∗22 −m2

2 +√E∗23 −m2

3

)2

The phase-space mechanism can then be simulated by uniformly sampling m212 and m2

23

under the constraint that (m223)min < m2

23 < (m223)max. The energy and momenta of all

three particles is then completely determined since p2 = E2 −m2:

E1 = (M2 +m21 −m2

23)/2M

E2 = (M2 +m22 −m2

13)/2M

E3 = (M2 +m23 −m2

12)/2M

As well as their relative angles:

cos(θij) =m2i +m2

j + 2EiEj −m2ij

2|pi||pj |

29

If we now take M to be the mass of a three-body system consisting of a core and two-

neutrons, we can add the decay energy Edecay to this system and distribute it amongst

the daughter products A − 2, n, and n. In this case, the three-body resonant lineshape

for the decay is taken to be an energy dependent Breit-Wigner, Eq. 2.6, and the energy

is distributed according to the above relations. For more than three products, a recursive

relation can be used to determine the momenta of the ith particle.

2.2.2 Sequential decay

The sequential model used in this analysis is based on the work of A. Volya [77, 78], which

uses the formalism of the Continuum Shell Model. Additional details beyond this outline

can be found in Ref. [77].

The sequential decay mechanism consists of multiple two-body processes. Consider a

level scheme like that in Figure 2.2. A nucleus with mass A has an unbound three-body

state with central energy E1 and width Γ1 relative to the ground state of the isotope with

mass A−2. The intermediate nucleus has a state defined with an energy E2 and and a width

Γ2 sufficiently narrow that its life-time is long enough to form the intermediate state. Let ε1

be the kinetic energy of the first neutron, and ε2 the energy of the second. Note that ε1,2 are

distributions and correspond to the decay energies in each step of the sequential mechanism

and are not necessarily equal to the energy difference between E1 and E2. Let E = ε1 + ε2,

denote an arbitrary three-body energy – distinct from E1 which is the centroid of the intial

state. For simplicity take E3 = 0.

In this formalism, a distribution for the relative energy of the two neutrons Er = ε1− ε2

is calculated as a function of the total decay energy E. The first neutron, with kinetic energy

ε1 decays from an initial state E1 to an intermediate unbound state E2, which also decays

30

P, MA

A-1

A-2

p1, m1

p2, m2

p3, m3

E

A A− 1 A− 2

ǫ1

ǫ2

E1,Γ1

E2,Γ2

E3 = 0

Figure 2.2: (Top) Schematic for a sequential decay. (Bottom) A hypothetical level schemewhere one would expect to observe a sequential decay. The hatched areas indicate widths.Note that the intermediate state is narrow and well separated from E1.

emitting another neutron with kinetic energy ε2. Assuming a spin anti-symmetric pair of

neutrons, the total amplitude for the decay becomes:

AT (ε1, ε2) =1√2

(A1(ε1)A2(ε2)

(ε2 − (E2 − i2Γ2(ε2))

+A1(ε2)A2(ε1)

(ε1 − (E2 − i2Γ2(ε1))

)(2.7)

Where A1 and A2 are the single-particle decay amplitudes.

Recall that the three-body energy is E = ε1 + ε2. We introduce S = E2 − E, the

difference between the intermediate state and the three-body energy. If S > 0, then the

level structure is like that illustrated in Fig. 2.3. For S < 0, the intermediate state is not

31

classically forbidden and we have a heirarchy like that illustrated Fig. 2.2. Eq. 2.7 can now

be rewritten as:

AT (ε1, ε2) =1√2

A1(ε1)A2(ε2)[S + ε2 − i2Γ2(ε1)] + A1(ε1)A2(ε2)[S + ε1 − i

2Γ2(ε2)]

[S + ε1 − i2Γ2(ε2)][S + ε2 − i

2Γ2(ε1)](2.8)

The single particle decay amplitudes are related to their widths by the following relation:

Γi = 2π|Ai(ε)|2

Which can be equated with the single-particle decay width γl(ε) multiplied by a spectroscopic

factor Si:

Γi = 2π|Ai(ε)|2 = γl(ε)Si

The single-particle width can be estimated for a neutron in a square well using the expression

derrived in Bohr-Mottleson Vol. I [79]:

γl =2~2

µR(kR)

∣∣∣∣2l − 1

2l + 1

∣∣∣∣Tl(kR)

Here Tl(x) is the tranmission probability through the centrifugal barrier. For s and p waves,

T0 = 1 and T1 = x2/(1 + x2). R ∼ 1.3(A+ 1)1/3 is the nuclear radius in fm, and k =√

2µε.

µ is the reduced mass and ε the incident neutron energy. To get to a decay rate and a cross

section, we need to utilize the Fermi Golden Rule which gives the partial decay width as:

dΓ(E)

dε1dε2= 2πδ(E − ε1 − ε2)|AT (ε1, ε2)|2 (2.9)

32

Putting the decay amplitudes in terms of the single-particle widths and applying Fermi’s

Rule 2.9, we obtain the following expression for the differential width in terms of the relative

energy Er = ε1 − ε2:

dΓ(E)

dEr=

1

8πγl(ε1)γl(ε2)

[E + 2S − i

2 [Γ2(ε1) + Γ2(ε2)]

[S + ε1 − i2Γ2(ε2)][S + ε2 − i

2Γ2(ε1)]

]2

The cross-section then follows the familiar Breit-Wigner form with the differential written

in terms of the relative energy:

dσ

dEr∝ 1

(E − E1)2 + Γ2T (E)/4

dΓ(E)

dEr

Where the total width ΓT (E) is obtained from:

ΓT =

∫dEr

dΓ(E)

dEr

In this manner, the relative energy distributions for the two neutrons are calculated

depending on the energy and widths of the states involved. Once the distribution for each

neutron is calculated, the process is treated as two two-body decays. In cases where S > 0,

the intermediate state is higher in energy than the three-body state and the decay proceeds

through it’s width.

It should be noted, that this formalism assumes that the two neutrons come from the

same single-particle orbital and are coupled to Jπ = 0+. In addition, although the Breit-

Wigner lineshape for the relative energies depends on the ` value of the three-body and

intermediate state, the angular distributions of the neutrons are assummed to be isotropic

in the rest frame of each two-body decay.

33

2.2.3 Di-neutron decay

The di-neutron model used in this analysis is also based on the work of A. Volya [77, 78].

In this model the di-neutron cluster breaks away from the core before decaying into two

separate neutrons.

P, MA

A-2 p3, m3

p1, m1

p2, m2

A A− 1 A− 2

E1,Γ1

E2,Γ2

E3

Figure 2.3: (Left) Schematic for dineutron emission. (Right) A hypothetical level schemewhere one would expect to observe a dineutron. The hatched areas indicate widths.

Let the dineutron have mass mD = 2m, and reduced mass µ = m/2. Define εK as the

kinetic energy of the dineutron. Let εI be the intrinsic energy of the dineutron - or neutron-

neutron energy, and E2 be the energy of the “intermediate state” which may be classically

forbidden. The total three-body energy is denoted by E1 = εK + εI . For simplicity take

E3 = 0. The decay is treated as a two-step process where the dineutron first separates from

the core and then decays into two neutrons. The amplitude for the decay is given by:

AT (εK , εI) =A1(εK)A2(εI)

εI − (E2 − i2Γ2(εI))

Where, A1 is the amplitude for the di-neutron emission and A2 is the amplitude for the

di-neutron breakup. Substituting this expression into Fermi’s Golden Rule 2.9, we obtain

the following for the differential width:

dΓ

dεKdεI=

1

2πδ(E1 − εK − εI)

Γ1(εK)Γ2(εI)

[(εI − E2)2 + Γ22(εI)/4]

(2.10)

34

Next, it is assumed that both the emission of the dineutron, and the subsequent breakup,

can be parameterized as an s-wave decay. In this case, the decay width for Γ2(εI) becomes:

Γ2(εI) =2~2

µr0kI

Where µ is the reduced mass of the dineutron and r0 is the channel radius, approximated

as r0 = 1.4(21/3) ∼ 1.7 fm. Likewise, the decay width for Γ1(εK) becomes:

Γ1(εK) =2~2

mDRkK

Here mD is the mass of the dineutron, and the channel radius R includes the size of the

core, R = 1.4[(A− 2)1/3 + 21/3]. To determine the intermediate energy E2, or virtual state,

we require consistency with the effective range approximation. Recall that in the s-wave

decay the decay width is proportional to√εI . As εI → 0 the denominator of the scattering

amplitude AT must behave like 1/as + ikI where as is the n−n scattering length, [78] (Note:

~2/µr0 = Γ2/2kI) thus:

limεI→0

[εI −

(E2 −

i

2Γ2(εI)

)]=

~2

µr0(

1

as+ ikI)

−E2 +

i

2Γ2(εI) =

Γ2(εI)

2kI

(1

as+

ikI

)E2 = −Γ2(εI)

2kIas

(2.11)

Substituting Γ2(εI) = 2~2µr0

kI , it follows that:

E2 = − ~2

µr0as

35

For a given scattering length, we can associate an energy:

ε0 =~2

2µa2s

So we may write:

E2 = −ε02asr0

Recall that εI and εK are defined as the following:

εK =~2k2K2mD

εI =~2k2I2µ

And we may express the widths as:

Γ1(εK) = 2|as|R

√ε0εK

Γ2(εI) = 4|as|r0

√ε0εI

Setting the masses to µ = m/2 and mD = 2m, substituting the widths into Eq. 2.10 and

integrating over εK we obtain:

dΓ(E1)

dε1=

1

π

√(E1 − εI)εI(

1 + r02as

εIε0

)2ε0 + εI

r0R

(2.12)

Which defines the distribution for the intrinsic energy of the dineutron. We can make an

approximation if εI << |2asε0/r0|. The n-n scattering length is as = −18.7 fm [80]. Using

r0 ∼ 1.7 fm, and ε0 ∼ 0.15 MeV gives us εI << 3 MeV. In this regime, we can approximate

36

the integral of Eq. 2.12 with the expression:

Γ(E1) =r0R

(E1

2+ ε0 −

√ε0(ε0 + E1)

)

However, integration of Eq. 2.12 is still performed numerically in simulation to determine

the energy distributions of the dineutron and its intrinsic energy.

37

Chapter 3

Experimental Technique

3.1 Experimental Setup

This section gives an overview of the experimental setup at the National Superconducting

Cyclotron Laboratory (NSCL) using the Modular Neutron Array (MoNA), the Large-area

multi-Institutional Scintillator Array (LISA), and the Sweeper magnet. The overall setup is

described here while the details of each detector are discussed in the following sections.

The experiment was performed at the NSCL, where a 140 MeV/u 48Ca beam impinged

upon a 1363 mg/cm2 9Be target to produce an 24O beam at 83.3 MeV/u with a purity of

∼ 30%. The A1900 fragment separator was used to select the 24O beam from the other

fragments in the secondary beam. The 24O beam continued on to the experimental area

where it impinged upon the Ursinus College Liquid Hydrogen Target [81], which was filled

with liquid deuterium (LD2). The average beam rate was approximately 30 particles per

second.

After the beam reacted in the target the resulting charged fragments were swept 43.3 by

a 4-Tm superconducting sweeper magnet [82] into a series of position and energy-sensitive

charged particle detectors. Inside the sweeper focal plane were two cathode-readout drift

chambers (CRDCs), separated by 1.55 m, an ion-chamber, a thin timing scintillator, and an

array of CsI(Na) crystals called the hodoscope. Fig. 3.1 shows a diagram of the experimental

setup.

38

y z

x

yz

x

MoNA-LISA

Beam

5m

Focusing Triplet

Target Scint.

LD2 Target

Sweeper

CRDCs

Ion Chamber

Thin Scint.

CsI(Na) Hodoscope

Figure 3.1: Layout of the detectors in the N2 Vault.

The neutrons produced from the decay of unbound states traveled undisturbed 8m to-

wards MoNA and LISA [83]. MoNA and LISA each contain 9 vertical layers with 16 bars

per layer and the combined array was configured into three blocks of detector bars. LISA

was split into two tables 4 and 5 layers thick, with the 4 layer table placed at 0 in front

of MoNA, while the remaining portion of LISA was placed off-axis centered at 22. The

resulting angular coverage in the lab frome was from 0 ≤ θ ≤ 10 for the detectors placed

at 0, and 15 ≤ θ ≤ 32 for the off-axis portion.

Together, MoNA-LISA and the sweeper magnet provide a kinematically complete mea-

surement of the neutrons and the charged particles from which the decays of unbound states

can be reconstructed. With the full 4-vector information of each particle, three-body corre-

lations can also be examined in cases where nuclei decay by emission of two-neutrons.

39

3.2 Beam Production (K500, K1200)

An 24O beam was provided by the Coupled Cyclotron Facility (CCF) [84] and A1900 Frag-

ment Separator at the NSCL [85]. The facility provides intense heavy ion beams, both stable

and unstable via fast fragmentation [86]. Since 24O has a half-life of 64 ms [87] it cannot be

accelerated directly. A diagram of the beam production process is shown in Figure 3.2.

Figure 3.2: Beam production at the Coupled Cyclotron Facility [84]. 48Ca is heated up inan ion-source and accelerated by the K500 and K1200 cyclotrons. After impinging on a Betarget, the fragments are filtered by the A1900 to provide the desired beam.

A beam of stable 48Ca was first accelerated to 140 MeV/u in the coupled K500 and

K1200 cyclotrons. After emerging from the K1200, the beam impinged upon a 1363 mg/cm2

9Be target where the fragmentation process occured. A wide variety of nuclei are made

simultaneously by this process. In order to isolate the 24O beam the A1900 separator was

used. The A1900 has four dipoles with focusing elements inbetween, to filter the fragmenta-

tion products by their rigidty Bρ = p/q to select a specific momentum to charge ratio. An

achromatic aluminum wedge with thickness 1050 mg/cm2 was placed inbetween the second

and third dipoles to improve separation. The energy loss through the wedge is proportional

to square of the nuclear charge, Z2. Hence different elements with the same rigidity entering

the wedge will have different rigidities upon exit. The 24O was delivered to the experimental

40

vault with an energy of 83.4 MeV/u corresponding to a rigidity of 4.0344 Tm at a rate of

∼ 0.6 pps/pnA. The largest contaminant was 27Ne which arrived with the same rigidity

at an energy of 122.4 MeV/u. In addition to the 24O beam, an 20O beam of much higher

intensity (∼ 700 pps/pnA) was also provided for calibration and diagnostics.

3.3 A1900 & Target Scintillator

At the end of the A1900 is a plastic timing scintillator located 10.579 m upstream from the

liquid deuterium (LD2) target in the N2 vault. It is made of 0.125 mm thick BC-404 and is

optically coupled to a PMT. The target scintillator, also made of BC-404, is 0.254mm thick

and was placed 1.0492 m upstream from the LD2 target and was coupled to a PMT. When

a particle passes through the plastic, it creates electron-hole pairs that recombine emitting

photons. These photons are then collected in the PMTs and converted to an electronic signal.

The signals from these detectors can be used to help separate beam contaminants by time-

of-flight measurement. In addition to the timing scintillators, the cyclotron radio-frequency

(RF) is also recorded to provide additional separation.

3.4 Liquid Deuterium (LD2) Target

This experiment opted to use a cryogenic deuterium target over deuterated plastics such as

CD2 for two main reasons: (1) a reduced carbon background, and (2) it provides higher

density of D2 for the same overall target thickness. The Ursinus-NSCL Liquid Hydro-

gen/Deuterium Target (LD2) offers a high-density, low-background deuteron target for a va-

riety of experiments including elastic scattering, secondary fragmentation, charge exchange,

and nucleon transfer. The basic principle of the LD2 target is simple: fill a volume with D2

41

gas and cool it so the liquid collects at the bottom of a target cell. The LD2 target consists

of five main components, described in the following sub-sections:

1.) Target Cell: Holds the liquid deuterium. Cylindrical in shape.

2.) Refrigerator System: A Sumitomo 205D Cryocooler.

3.) Vacuum Chamber: Houses the target cell, cold finger, refrigerator and heat shield.

4.) Temperature Control System: Monitors the temperature of the target cell and regulates

the temperature of the heater block.

5.) Gas handling system: Regulates the flow of neon, hydrogen or deuterium to the refrig-

erator.

Figure 3.3: Schematic of the Ursinus College Liquid Hydrogen Target. (Left) A head onview along the beam axis. (Right) Side view.

42

Gas Boiling Point Triple PointHydrgoen (20.35 K, 760 Torr) (13.85 K, 54 Torr)Deuterium (23.50 K, 760 Torr) (18.70 K, 128 Torr)Neon (27.07 K, 760 Torr) (24.56 K, 323 Torr)

Table 3.1: Boiling and triple points of hydrogen, deuterium, and neon.

Including the resevoir in the gas handling system, a total of 100 L of hydrogen or deu-

terium at STP is contained in the entire apparatus. The target operates by filling the target

cell with an appropriate amount of gas and cooling it to near the triple point, where the gas

condenses to the liquid state. Table 3.1 documents the triple points for neon, hydrogen, and

deuterium. For deuterium, the triple point is at approximately 18.7 K and 128 Torr. During

operation, the target was held at roughly 20 K and ∼850 torr. This lies in the window

between the solid-liquid, and liquid-gas phase transitions of D2 as seen in Fig. 3.4.

[K]calT10 12 14 16 18 20 22 24 26 28 30

[to

rr]

cal

P

800

850

900

950

1000

1050

1100

1150

1200

1250

1300

Figure 3.4: Phase diagram for deuterium. The solid line marks the liquid/solid transition,while the blue dotted line denotes the liquid/gas transition. The plus marks are data obtainedduring the initial filling of the target.

As seen by the schematic of the target in Fig 3.3, the deuterium fills the entire volume of

the gas line which is connected to the target cell resting in the beam path. The cryocooler,

which sits on top, cools the deuterium gas until it condenses and drips down the gas line

43

into the target cell. However, since the cooler is operated by a closed liquid He cycle, it

will cool the D2 to 4 K, which would cause the liquid to freeze and clog the gas line. For

this reason the target cell is coupled to a heater block which counter-acts the cryocooler to

maintain the temperature of the liquid at a desired point. The temperature is read out by

two silicon diodes, one attached to the target cell, and another attached to the heater block.

The pressure is read out by a monometer in the gas handling system, which is connected to

the target cell line.

3.4.1 Target Cell

The target cell is cylindrical with a diameter of 5.4 cm and a length of about 3.0 cm, and

consists of an aluminum frame with Kapton windows 125 µm thick on both ends. It is

designed to hold the liquid deuterium in place. For the cell used in this experiment, the

design thickness for deuterium was 400 mg/cm2, or 200 mg/cm2 for hydrogen. The cell

couples to a commercial refrigerator, and has a diode attached to the frame for reading out

the temperature. A photo of the cell along side a mechanical drawing can be found in Fig.

3.5

The cell is designed to withstand an outward pressure gradient of about 2 atm as it sits in

a vacuum. When the target cell is filled, the kapton foils bulge outward increasing the actual

thickness of the deuterium. The cell is surrounded by a heat shield to reduce the thermal

load and enable cooling from room temperature to the triple point. To ensure temperature

stability during the experiment, the openings in the heat shield were covered with 5 µm thick

aluminized reflective mylar film.

44

Figure 3.5: (Left) Photo of the target cell used to contain the Liquid Deuterium. The liquiddrips down through the center hole seen on the target flange. The iridium seal can be seensurrounding it before being pressed. (Right) Drawing of the inner ring where the Kaptonfoil is glued. The ring is then clamped to the target by an outer ring visible in the left photo.

3.4.2 Temperature Control System

The temperature of the target cell is regulated by the heater block. Since the target cell

sits in a vacuum during operation, heat can only be transfered by thermal radiation or

conduction. The heater block is controlled by a Lakeshore 331S temperature controller unit

which is operatated manually by a PC running LabView. The Lakeshore 331S controller

reports the diode temperature as a voltage which is then read out by the Experimental

Physics and Industrial Control System (EPICS) [88] and later converted to Kelvin. Details

of the LabView programming and operation of the temperature control system can be found

in the Liquid Deuterium Target users manual [89].

The temperature controller unit relies on a feedback loop to maintain a desired equillib-

rium. Because the heater block is not in direct contact with the target cell, there is thermal

lag between it and the target cell. The time it takes for the heater block to affect the cell

is too long to use the diode at the target cell in a feedback loop. Instead the temperature

of the cell must be monitored, and controlled from a separate diode attached to the heater

block. This often means that the “set point”, or desired temperature, of the heater block

45

is different from the desired temperature in the cell. However, during liqufication, the cell

temperature is closely monitored to determine an appropriate set point.

3.4.3 Gas Handling System

The gas handling system controls the flow of air, deuterium and dry nitrogen when evacuating

and filling the target. It is designed with safety as a priority, and its purpose is to regulate

the flow of these gases to insure that the mixture of deuterium and nitrogen/air stays well

below the flammabilty limit, and that there is never an over-pressure on the target cell which

may cause it to implode. A schematic of the gas handling system is shown in Fig. 3.6. Table

3.2 describes each of the components. The full operation of this system and the LD2 target is

describted in the LHDT Users Manual [89]. The target pressure is read out by a manometer

attached to the target cell line. This manometer reports a voltage which is then read out by

EPICS.

3.4.4 Vacuum Chamber

The vacuum chamber holds the target assembly in the beam line and interfaces with the

existing beam-line structure. It was connected directly to the flange of the sweeper magnet,

and to the target-scintillator. Due to the height of the target, and the geometry of the

sweeper magnet, the entire target had to operated at a 30 angle. This resulted in only a

portion of the target cell being filled. However the target itself was much larger than the

beam-spot, ensuring that the tilt had no effect.

The bellows beneath the cryocooler, illustrated in Fig. 3.3, allow for adjusting the target

cell position in the beam line. Using a laser alignment, the cell was centered on the beam-

46

Component Function

Target Cell Cell containing LH2 or LD2.Reservoir 100 L tank which serves as H2 or D2 reservoir.H2 Pressurized gas bottle with H2 or D2.T (B141TP)/ B141GV Turbo-pump / Turbo gate valve.P Pascal C2 series 2015 C2 rotary pump.V1,3,4,5,10 Manual valves.V2 Needle valve.V6,7 Manual needle valves on flowmeter F1 and F2.V8 (B141FV) Fore valve.V11 (B141VV) Venting valve.F1 Flowmeter for H2/D2 gas (always open).F2 Flowmeter for dry nitrogen (always open).R1 Regulator for gas bottle.M1,3 Manometers with a range of 1 - 5000 Torr.

M1 reads the cell pressure, and M3 the pressure in the reservoir.M2 Manometer for the gas cell with a range of 0.001 - 1 Torr.M4 (B142PG) Pirani gauge and ion gauge for beam-chamber vacuum.N2 Exhaust Line Exhaust line for discharging the H2/D2 gas.Dry Nitrogen (DN) Dry Nitrogen Supply.Dry Nitrogen/Vent Vent line for the target system with dry nitrogen.

Table 3.2: List of components in the gas handling system. Table adopted from Ref. [89].

47

Figure 3.6: A diagram of the gas handling system used to control the flow of deuterium inand out of the target cell. Figure adopted from [89]

axis and the foils were aligned perpendicular to the beam by lining up the reflection of the

laser off the back of the second foil with the impinging beam-spot.

3.5 Sweeper Magnet

The sweeper magnet is a large-gap superconducting dipole magnet with a bending angle of

43.3 and a radius of 1 meter [82]. It’s purpose is to sweep charged particles and unreacted

beam away from MoNA-LISA and towards a suite of charged-particle detectors described in

the following sections. The charged reaction products exiting the target are swept away while

48

the neutrons continue straight through a vertical gap of 14 cm towards MoNA-LISA. The

maximum rigidity of the sweeper is 4 Tm. The magnetic field in the sweeper is monitered

with a Hall probe and the dipole field has been mapped in previous work [90]. For reactions

with the 24O beam, the magnet was set to a current of 320 A, corresponding to a central

rigidity of 3.524 Tm. To measure the background induced by the kapton foils of the target,

as well as diagnose the sweeper, the LD2 target was put in a gaseous state by warming it to

50 K. This reduces the thickness of the deuterium to ∼ 1 mg/cm2. For the settings with the

warm gaseous target, the current was raised to 360 A to account for the more rigid beam.

The central rigidity on those setting was 3.85 Tm.

3.6 Charged Particle Detectors

Immediately following the sweeper magnet was a collection of charged particle detectors

residing in a vacuum box. The position of the reaction products deflected by the magnet

was measured with two Cathode Readout Drift Chambers (CRDCs) separated by 1.55 m.

Following the CRDCs was an ion-chamber which provided a measurement of energy loss,

and a thin (5 mm) dE plastic scintillator which triggered the system readout and gave a

time-of-flight measurement. Finally, an array of CsI(Na) detectors consisting of 25 crystals,

each 80 x 80 x 25 mm3 was installed behind the thin scintillator and stopped the fragments

while measuring their total energy.

3.6.1 CRDCs

The first CRDC was placed approximately 1.56 m from the target, where the distance is

measured along the central track of the dipole, and the second CRDC was placed 1.55 m

49

downstream of the first. The CRDCs measure the X and Y position, from which the angle of

the particles can be determined and their path traced backward to the target. A schematic

of the detector can be found in Figure 3.7.

(A,Z)

xz

ye−

Cathode PadsFrisch Grid

Anode Wire

−E

Figure 3.7: Schematic of a Cathode Readout Drift Chamber (CRDC) where the z-directionhas been expanded. The field shaping wires are not drawn for visibility. Note that theelectron avalance is does not begin until the electrons encounter the Frisch grid.

The CRDC is similar to an ion-chamber. It is filled with a 1:4 mixture of isobutane

and CF4 gas at a pressure of 40 torr and sealed with two windows. When a particle passes

through the gas it creates ionization pairs which drift apart due to a uniform applied electric

field. This field is created by the application of a drift voltage of 1000 V between a plate at

the top of the detector, and a Frish grid near the bottom of the detector. Field shaping wires

are placed at specific intervals along each face of the detector parrallel with the X direction.

50

Under the Frisch grid is an anode wire (parallel with the X direction) and a collection of 116

aluminum cathode pads with a pitch of 2.54 mm in width segmented along the X direction.

When electrons drift into the Frisch grid they enter a strong electric field created by the

anode wire causing an avalanche of electrons. The Y-position of the interaction is determined

by the drift time of the electron, which is defined as the difference between a signal in the

thin timing scintillator and a signal on the anode wire. The X-position is determed from the

induced charge distribution on the cathode pad caused by an avalanche of electrons. The

peak of this distribution gives the X-position of the particle. The Z-position is assumed to

be the center of the detecting volume along the beam axis since there is no segmentation in

this direction. The active area of each CRDC is 30 x 30 cm2 in the XY plane.

3.6.2 Ion Chamber

The ion-chamber is a gas-filled detector similar to the CRDCs but segmented in the Z-

direction with 16 pads. The active volume of the detector is 40 x 40 x 65 cm3. The ion-

chamber is filled with P-10 gas (10% CH4 and 90% Ar2) and held at 300 torr. The windows

are made of Kevlar filament and 12 µm PPTA and are mounted with epoxy. They allow

particles to pass through with neglible energy loss. The upstream window has an active area

of 30 x 30 cm2 to match the acceptance of the CRDC, while the downstream window is 40

x 40 cm2 to allow for dispersion of the beam.

The ion-chamber has a plate on top and 16 charge collecting pads on the bottom biased

to create a drift voltage of 800 V. When a charged particle enters the gaseous volume of the

detector, ionization pairs are created and the electrons are collected on the 16 pads. The

energy loss in the gas can be calculated from the total charge collected on all 16 pads.

51

z x

y

Light Guides

PMT 2 PMT 0

PMT 3 PMT 1

Scintillator

Figure 3.8: (Left) Head-on view (looking into the beam) of the thin timing scintillator.(Right) An example level scheme for transitions in the organic material with a π-electronstructure. Source: [91]

3.6.3 Timing Scintillators

The thin timing detector rests inbetween the ion-chamber and the hodoscope. It is a plastic

scintillator (EJ-204) with dimensions of 55 cm x 55 cm x 5mm and has pairs of photomulti-

plier tubes attached via light guides on the top and bottom of the detector. It measures the

time-of-flight and triggers the data aquisition system. A schematic of the detector is shown

in Fig. 3.8. The light guides are trapezoidal and optically connected to the PMTs.

When a charged particle passes through the organic scintillator it deposits energy into

the material. A small portion of this kinetic energy is converted into flourescent light, while

the majority is dissapated non-radiatively through lattice vibrations or heat. The floures-

cence arises from transitions in the energy level structure of a specific molecule, in this case

Polyvinyl-toluene doped with antracene. Plastic scintillators such as these take advantage

of the π-electron structure of these molecules. The typical spacing of vibrational states in

organic scintillators is on the order of 0.15 eV, which is much greater than the average ther-

52

mal energy at room temperature kT = 0.025 eV, meaning nearly all the molecules are in the

ground state. The typical spacing of the singlet states is on the order of a few eV. Fig. 3.8

shows a level scheme for an organic molecule with a π-electron structure. When a charged

particle passes by, it excites the molecule to one of the singlet states. The principle source

of flourescence comes from the de-excitation of the first-excited singlet state S1 by internal

conversion to one of the vibrational states of the ground state S0x. Any state with excess

vibrational energy quickly loses that energy as it is no longer in equillibrium with its neigh-

bors. This decay is called prompt flourescence and is typically on the order of nanoseconds.

For EJ-204, the decay constant is 1.8 ns.

It is also possible to decay to a triplet state which can be longer lived, with lifetimes

up to 10−3 s, causing a delayed emission of light with a longer-wavelength since the triplet

state is a lower energy than the singlet. This, along with multiple available excited states,

causes a spectrum of light to be emitted. The emission spectrum for EJ-204 is shown in Fig.

3.9, and peaks around 410 nm [92]. The light emitted in the de-excitation of the organic

molecules scatters within the plastic until it is collected in the PMTs [91].

Figure 3.9: Emission spectrum for EJ-204. The peak wavelength is around 410 nm [92].

53

3.6.4 Hodoscope

The last detector in the sweeper focal plane is the hodoscope. The hodoscope is an array

of CsI(Na) detectors consisting of 25 3.25” x 3.25” x 2.16” crystals oriented in a 5 x 5

square. A mechanical design of the detector is shown in Figure 3.10. The array is assembled

with 5 rows which each contain 5 crystals and is centered on the central track through the

sweeper. Each crystal is wrapped in reflective material 0.2 mm thick, and optically coupled

to a Hamamatsu PMT R1307 with magnetic shielding. There is no light guide between the

PMT and the crystal. The hodoscope fully stops the charged particles due to its thickness

and measures their remaining energy.

Figure 3.10: Schematic of the Hodoscope, which is an array of CsI(Na) crystals arranged ina 5x5 configuration.

The scintillation mechanism depends on the energy states determined by the crystal

lattice of CsI. Electrons only have available discrete bands of energy in insulators or semi-

conductors. When a charged particle passes through the lattice, electrons are excited from

54

the valence band across the forbidden region into the conductance band which leaves an

electron hole. A return of an electron to the valence band can cause the emission of a pho-

ton. However for pure crystals this is an inefficient process so often a dopant or impurity

is introduced. The added impurity can create available states in the forbidden band of the

crystal which increases the probability of populating and de-excitating from these states

since their energies are less than the full forbidden gap. CsI(Na) typically has a slow decay

time which consists of two components with mean lives of 0.46 µs and 4.18 µs. In addition,

CsI(Na) is hydroscopic so care must be taken to avoid exposure to the ambient atmosphere.

A four-sided gas cover surrounds the crystals and an inlet allows dry nitrogen to flow over

the face of the crystals whever the detector box is not under vacuum.

3.7 MoNA LISA

The Modular Neutron Array (MoNA), and the Large-area multi-Institutional Scintillator

Array (LISA) each consist of 144 200 x 10 x 10 cm3 plastic scintillator bars. Each bar in

MoNA is made of BC-408, while LISA is made of EJ-200. The bars are wrapped in reflective

material and black plastic to reduce light loss and prevent ambient light from leaking in.

Each bar is also coupled to two PMTs on either end by light guides. The MoNA-LISA bars

serve to measure the position and time-of-flight of neutrons that interact in the plastic. When

a neutron scatters off hydrogen or carbon nuclei in the bar, scintillation light is produced

and the photons internally reflect until they are collected by the PMTs. The position along

the bar is determined by the time difference of the two PMTs, and the interaction time is

determined from their average. The Y and Z coordinates are given by the discretization of

the bars.

55

Figure 3.11: 12C(n,*) cross sections for neutron energies ranging from 1 - 100 MeV for severaldifferent reactions. Each of the cross sections listed here are included in MENATE R andused to model the neutron interactions in MoNA-LISA. Image source: [93]

When a neutron enters the plastic it interacts with carbon or hydrogen nuclei causing

them to scatter which excites the plastic causing flouresence in a manner described in section

3.6.3. Figure 3.11 shows different cross sections as a function of neutron kinetic energy. At

typical beam energies, it is most likely for neutrons to interact inelasticlly with carbon since

the elastic cross section for H(n,p) drops as the neutron energy increases. However, since the

mass of a carbon nucleus is much larger than that of hydrogen, the recoil is much smaller,

and so less light is produced in the plastic compared to scattering on hydrogen. Thus the

dominant signal comes from scattering on hydrogen. The emitted light scatters towards the

ends where it is collected by a PMT. MoNA and LISA use Photonis XP2262/B PMTs and

Hamamatsu R329-02 PMTs respectively.

56

3.8 Electronics and DAQ

The data acquisition (DAQ) system for MoNA, LISA, and the sweeper magnet is described

in detail in References [90, 94, 95, 96]. An overview is presented here, with an abbreviated

schematic in Fig. 3.12. Each detector subsystem runs an independent acquisition system

connected by a “Level 3” system which generates a system trigger and a timestamp to be

relayed to each detector. After the data are written to disk, the seperate files for each

subsystem are merged by matching timestamps event-by-event. The system trigger in this

experiment was the left-upper PMT of the thin scintillator (PMT 0), and the timestamp

was a 64-bit word generated by the clock of the Level 3 system.

The trigger logic was handled by Xilinx Logic Modules (XLMs), divided into 3 levels.

The Level 1 and Level 2 XLMs determine weather or not an event in MoNA or LISA is valid,

with a valid event being defined by a good timing signal in the CFD channels for both PMTs

in a single bar. Level 3 contains a clock which runs when the system is not busy processing

an event, and handles the coincidence trigger logic between MoNA-LISA and the Sweeper.

Upon recieving a signal from the system trigger, the Level 3 system opens a coincidence gate

of 35 ns and waits for a valid signal from either MoNA or LISA. If one is recieved a “system

trigger” signal is sent to each subsystem and the event is processed. If no such signal is

recieved, then the coincidence gate will close and the system will fast clear. If MoNA-LISA

trigger but not the sweeper, then they will send a trigger and busy signal to Level 3 causing

it to go busy and reject signals from the sweeper. Without a signal from the sweeper, the

system trigger cannot be produced, and the coincidence gate is never opened. Since MoNA

and LISA do not recieve a system trigger in this case, they fast clear.

MoNA and LISA each consist of identical but independent electronic set-ups. Each PMT

57

has two outputs, an anode and a dynode. The anode signal is used for local triggering and

for timing, while the dynode is used to measure the charge collected in the PMT. The timing

signal proceeds to a constant fraction discriminator (CFD). The timing signals from both

PMTs then go from the CFD to a time-to-digital converter (TDC) and an XLM module.

The TDC modules are run in common stop mode, meaning a trigger in MoNA/LISA will

signal the start, with the stop coming from the Level 3 system trigger. Finally, the charge

signal from the dynode goes to a charge-to-digital converter (QDC) for integration. This

process is duplicated for every bar in MoNA and LISA.

In the sweeper, the electronics are set up for three timing scintillators, two CRDCs,

an ion-chamber, and a CsI(Na) array. Each timing signal from the thin PMTs, target

scintillator, and A1900 scintillator goes to a CFD and then a TDC. In the case of the thin,

the timing signal from PMT 0 is sent to Level 3 to act as the system trigger. Where charge

signals are available, they are sent to amptlitude-to-digital converters (ADCs). All TDCs in

the sweeper operated in common start mode. The Level 3 trigger began the measurement,

and the timing signal itself provided the stop. The pads of the CRDCs were digitized by

Front-End-Electronics (FEE) modules that sampled the pulse and sent it to an XLM. For

the ion chamber, the signals from each pad were sent directly to a shaper and then to an

ADC. Finally, the PMT signals from the CsI(Na) array, or Hodoscope, went through shaping

amplifiers and then ADCs. Every time the system recieved a trigger from Level 3, all TDC,

ADC, QDC and XLMs were read out and processed.

58

PMT

CFD

QDC

TDC

Level 1

Level 2

MoNA-LISA

Thin Scint.

Target Scint.

A1900 Scint.

CRDC

Ion Chamber

Hodoscope CsI(Na)

CFD TDC

ADC

CFD TDC

ADC

CFD TDC

FEE XLM

ADC

ADC

ADC

Sweeper

Sweeper Trigger

Trigger

Gate

Level 3

LegendStart

Stop

Gate

1

Figure 3.12: Schematic of the electronics for MoNA-LISA and the Sweeper. Dashed linesencompases each subsystem. Green arrows indicate start signals, red stop signals, and bluearrows indicate the QDC/ADC gate for integration. Upon receiving the system trigger fromlevel 3, all TDCs, QDCs, and ADCs read out and are processed.

59

3.9 Invariant Mass Spectroscopy

Consider the decay of a particle with mass M into a large fragment A and N neutrons, with

masses MA and mn respectively. Energy and momentum are conserved, thus:

EM = EA +i=N∑i=1

En

and

P νinitial = P νfinal

The quantity M2 = (P ν)2 is lorentz invariant, and therefore independent of reference

frame. The decay energy of an unbound nucleus is defined as the energy difference between

the initial nucleus and it’s decay products:

Edecay = MA+n −MA −i=N∑i=1

mn (3.1)

where MA+n is the invariant mass of the initial nucleus, MA the rest mass of the fragment,

and mn the rest mass of a neutron. The 4-vector of the initial nucleus is obtained by summing

the 4-vectors of all daughter products, which determines MA+n. In the case of a one-neutron

decay this expression becomes:

Edecay =√M2A +M2

n + 2(EAEn − ~pA · ~pn)−MA −mn (3.2)

For two-neutron emission, the expression becomes slightly more complicated:

Edecay =√M2T + 2(ET − ~pT

2)−MA − 2mn

60

Where

M2T = M2

A + 2m2n

E2T = EAEn1 + EAEn2 + En1En2

and

~pT2 = ~pA · ~pn1 + ~pA · ~pn2 + ~pn1 · ~pn2

While the decay energy simplifies to a single algebraic expression in the case of one, or even

two neutrons, an expression like 3.1 can become cumbersome in cases of 3 or 4 neutron

emission due to an abundance of cross-terms. It is much easier in those cases to handle the

4-vectors of each particle numerically to calculate dot products.

3.10 Jacobi Coordinates

In the case of three-body decays, or two-neutron emission, one can utilize Jacobi coordinates

to examine correlations between the neutron pair and the core. The Jacobi coordinate

system has the advantage of removing the center-of-mass motion so that the relative motion

is exposed. Given three particles, there are three unique coordinate systems that can be

chosen. However, since the neutrons are indistinguishable this reduces to two choices: the T

and the Y systems illustrated in figure Fig. 3.13. The vector ~kx is drawn from the second

particle to the first, and the second vector ~ky from the third particle to the center-of-mass

of the two-body subsystem. The relative motion of the three-body system can be described

by an energy ε, and angle θk defined as [2]:

ε = Ex/ET

61

cos(θk) = ~kx · ~ky/(kxky)

where ε is the energy of the two-body subsystem relative to the total three-body energy, and

cos(θk) the angle between the vectors kx and ky. More explicitly:

ET = Ex + Ey =(m1 +m2)k2x

2m1m2+

(m1 +m2 +m3)k2y2(m1 +m2)m3

where ~kx and ~ky are defined as:

~kx =m2

~k1 −m1~k2

m1 +m2

~ky =m3( ~k1 + ~k2)− (m1 +m2) ~k3

m1 +m2 +m3

And mi and ki denote the mass and momentum of each particle in the three-body system.

In the T system ε is the energy of the neutron-neutron pair relative to the total three-

body energy, whereas in the Y system it is the neutron-core energy. Additional information

on Jacobi coordinates can be found in Ref.[2] and Ref.[75]. The Jacobi Coordinates are a

1 2

322O

n nθk

ǫnn

kx

ky

T System

3

1

222O

n

n

θkǫfn

ky

kx

Y System

Figure 3.13: Jacobi T and Y coordinates for the three-body system 22O + 2n.

62

powerful experimental tool as they distinguish between the different decay modes a two-

neutron (or two-proton) unbound system can undergo. For example, in a di-neutron-like

correlation the two-neutrons are clustered together and so the angle θk is close to π in the

Y system and cos(θk) peaks at -1. In addition, the neutron-neutron energy is low relative

to the total three-body energy causing ε to peak at 0 in the T system.

For a sequential decay it is neccessary to make the distinction between the limiting cases

of “even” and “uneven”, as they have very different correlations. In an even sequential decay,

the intermediate state is at half the total three-body energy, and so both neutrons decay

with similar energy. Whereas in an uneven decay, the intermediate state is either close to

the three-body state or the final state, resulting in a high and a low energy neutron. Due to

the varying energies between the two cases, the corresponding three-body correlations are

dramatically different, as illustrated in Fig. 3.14.

Since a measurement of the decay energy is kinematically complete, the Jacobi spectra

can also be constructed from the measured 4-vectors of the two neutrons and the core.

Measuring the three-body correlations allow one to connect to the three-body wavefunction

as the few-body Schrodinger equation can be solved in the same coordinate system and

predictions made for the three-body decay. Three-body correlations in both the T and Y

are shown in Fig. 3.14 for the different cases of sequential (uneven/even), di-neutron, and

phase space decays. Effects from neutron scattering have been removed, illustrating the

stark difference between the different decay modes.

63

T/ExE0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Co

un

ts ­

T s

yste

m

)kθcos(­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 1

Co

un

ts ­

T s

yste

m

T/ExE0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Co

un

ts ­

Y s

yste

m

)kθcos(­1 ­0.8 ­0.6 ­0.4 ­0.2 0 0.2 0.4 0.6 0.8 1

Co

un

ts ­

Y s

yste

m

Uneven Sequential

Even Sequential

Di­neutron

Phase Space

Figure 3.14: Simulated Jacobi T and Y coordinates for the three-body system 22O + 2nwith ET = 750 keV. Effects from neutron scattering have been removed. Acceptances andefficiencies are applied. The different colors indicate different decay mechanisms. All spectraare normalized to 2 ∗ 106 events.

64

Chapter 4

Data Analysis

This chapter details the procedures and methods used to calibrate MoNA, LISA, and the

detectors in the Sweeper setup and how meaningful data are obtained from the raw signals

in each detector. After the calibrations are complete, event selection is discussed in addition

to modeling and simulation.

4.1 Calibrations and Corrections

4.1.1 Charged Particle Detectors

Following the sweeper magnet are several charged-particle detectors: two CRDCs, an ion-

chamber, a thin scintillator and a hodoscope. The following sections detail the calibration

procedures for these detectors including the timing scintillators upstream of the target.

4.1.1.1 CRDCs

The Cathode Readout Drift Chambers (CRDCs) provide a measurement of the X and Y

position of charged particles passing through the detector. They are used to track the

reaction products for isotope separation and to determine their energy and momentum at

the target. Hence, good tracking is essential for a successful reconstruction. There are two

CRDCs in the sweeper focal plane. CRDC1 was placed roughly 1.56 m from the center of

the LD2 target (along the center track), and CRDC2 was placed 1.55 m behind CRDC1.

65

CRDC1 CRDC2Bad Pad 96-100 24

104 121106

Table 4.1: Bad pads in the CRDCs which are removed from analysis.

The X position is determined by charge collection along 116 segmented pads with a pitch

of 2.54 mm in width. First, the quality of each pad must be examined. Bad pads that

show poor charge collection and give erroneous signals must be removed. Small leakage

currents in the CRDCs can be read out in the electronics, even with no beam. This signal is

called the pedestal and must be subtracted to properly determine the total charge collected.

The pedestal subtraction for CRDC1 and CRDC2 is shown in Figure 4.1, a gaussian fitting

algorithm is used to determine the pedestal for each pad. From the subtraction several

pathological pads can be identified; they are listed in Table 4.1.

After the pedestal-subtraction the pads need to be gainmatched. This is accomplished

using a “continuous sweep” run where the beam is moved across the detector to illuminate all

pads within acceptance. An 20O beam with 99% purity was used for this purpose. The pad

with the maximum charge deposited was selected event-by-event. The charge distribution

of each pad, when it registered as the maximum pad, was then gainmatched to a reference

(pad 64) with the following relation:

m =µrefµi

where µi is the centroid of the charge distribution on the ith pad. Figure 4.2 shows a

comparison before and after the gainmatching procedure. The total charge collected on the

66

pad #0 20 40 60 80 100 120

ped

esta

l (ar

b.)

0

100

200

300

400

500

600

700

800

900

1000

pad #0 20 40 60 80 100 120

ped

esta

l (ar

b.)

0

100

200

300

400

500

600

700

800

900

1000

pad #0 20 40 60 80 100 120

(ar

b.)

pad

Q

0

20

40

60

80

100

120

140

pad #0 20 40 60 80 100 120

(ar

b.)

pad

Q

0

20

40

60

80

100

120

140

Figure 4.1: Pedestal subtraction in the CRDCs. The raw pads for CRDC1 (left) and CRDC2(right) are shown in the first and second panels from the left, while the subtraction is shownin the third and fourth panels.

67

pad is determined by a Riemann-sum:

Qpad =1

n

n∑i=0

qi − qpedestal

where n is the number of samples and qi is the amount of charge per sample. The gain-

matched signal is then:

Qcal = m ∗Qpad

The X-position is then determined by the charge distribution across all pads. A gaussian

line-shape is fit to this distribution to determine the central value.

The Y-position is determined by the drift-time of the charge carriers in the active volume

of the detector. Thus, the drift time and pad-distribution need to be converted into physical

X and Y positions in the lab-frame. This is accomplished using tungsten masks with specific

hole-patterns drilled into them. The mask is placed in front of the detector and the known

hole-pattern can be used to determine a linear transformation from charge/time to X/Y

position.

It should be noted that the CRDCs are placed in opposite orientations in the x direction.

For CRDC1 the pad number increases in the +x direction in the lab frame, while for CRDC2

increasing pad numbers are in the−x direction. This results in their X slopes having opposite

sign.

The tungsten masks are put in place by a hydraulic drive. During the experiment, the

drive for CRDC2 was unable to fully lift the mask into position thus not covering the full

face of the detector. The X-slope is determined by the pitch of the pads, and the offset found

from the mask. The Y-slope is found from the spacing of the vertical holes, and likewise the

offset from the absolute position of the holes. However, since the mask did not fully insert,

68

pad #0 20 40 60 80 100 120

(ar

b.)

raw

Q

0

500

1000

1500

2000

2500

3000

pad #0 20 40 60 80 100 120

(ar

b.)

raw

Q

0

500

1000

1500

2000

2500

3000

pad #0 20 40 60 80 100 120

(ar

b.)

pad

Q

0

100

200

300

400

500

600

700

pad #0 20 40 60 80 100 120

(ar

b.)

pad

Q

0

100

200

300

400

500

600

700

Figure 4.2: Before (left) and after (right) gainmatching of CRDC1 and CRDC2. CRDC1 isshown in the first and third panel, and CRDC2 in the second and fourth.

69

Xslope [mm/pad] Xoffset [mm] Yslope [mm/ns] Yoffset [mm]CRDC1 2.54 -171.3 -0.1953 98.5CRDC2 -2.54 187.3 -0.2043 103.7

Table 4.2: Slopes and offsets for the CRDC calibration.

this means that the y-offset for CRDC2 cannot be determined by this method. Figure 4.3

shows 3 different mask-calibration runs taken at different points during the experiment, the

upper edge of the mask becomes visible, and it is evident the mask did not fully insert.

There was no indication of this occurring for the mask of CRDC1.

The y-offset of CRDC2 was determined by examining the decay-kinematics of 23O →22O + 1n, since the offset will not prevent isotope separation but will affect the fragment

energy. This offset was constrained by lining up the reconstructed fragment angles with the

neutron cone and matching the fragment and neutron energies. This procedure is iterative

since an offset must first be guessed. The parameters for this decay are shown in Sections

4.3 and 4.4. The slopes and offsets for both CRDCs can be found in Table 4.2.

The CRDCs can exhibit a drift in the measured Y position. The apparent Y-position can

fluctuate if the gas-pressure changes, or if the drift voltage fluctuates. This is corrected by

gain-matching the raw drift time to a reference run (Run1035), and performing a run-by-run

correction. The correction factor is determined by:

m =µTACref

µi

where µTACref and µi are the centroids of the TAC signal in the CRDC for the reference

run and an arbitrary run respectively. The corrected drift-time is simply:

tcorr = m ∗ tdrift

70

[mm] (lab)crdc2X­150 ­100 ­50 0 50 100 150

[m

m]

(lab

)cr

dc2

Y

­150

­100

­50

0

50

100

150

[mm] (lab)crdc2X­150 ­100 ­50 0 50 100 150

[m

m]

(lab

)cr

dc2

Y

­150

­100

­50

0

50

100

150

[mm] (lab)crdc2X­150 ­100 ­50 0 50 100 150

[m

m]

(lab

)cr

dc2

Y

­150

­100

­50

0

50

100

150

Figure 4.3: (From left to right) Mask runs 3023, 3078, and 3142 for CRDC2. Particles thatilluminate an area above the mask indicate that the mask did not fully insert.

71

Figure 4.4 and 4.5 shows this correction for CRDC1 and CRDC2. The drift in the CRDCs

is correlated because the two detectors are connected to the same gas-handling system.

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[m

m]

po

sY

­200

­150

­100

­50

0

50

100

150

200

Uncorrected CRDC1 Y

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[m

m]

po

sY

­4

­2

0

2

CRDC1 Y Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[m

m]

po

sY

­200

­150

­100

­50

0

50

100

150

200

Corrected CRDC1 Y

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[m

m]

po

sY

­4

­2

0

2

CRDC1 Y Centroid

Figure 4.4: Drift correction for CRDC1 Y position. (Top left), Uncorrected Y distributionin CRDC1 as a function of Run Number. (Top right), Uncorrected centroids of CRDC1 Yposition as a function of Run Number. (Bottom left). Corrected Y distribution in CRDC1.(Bottom right) Centroids of corrected Y distribution in CRDC1 as a function of run number.

4.1.1.2 Ion Chamber

The ion chamber is segmented into 16 pads along the z-axis, or beam direction. The raw

charge collected on each pad can be used for element separation, however each pad needs

to be gainmatched and any X or Y-position dependencies removed. To gainmatch the ion

chamber a beam was sent down the center of the detector. For this experiment, an 20O

72

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[m

m]

po

sY

­200

­150

­100

­50

0

50

100

150

200

Uncorrected CRDC2 Y

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[m

m]

po

sY

­4

­2

0

2

CRDC2 Y Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[m

m]

po

sY

­200

­150

­100

­50

0

50

100

150

200

Corrected CRDC2 Y

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[m

m]

po

sY

­4

­2

0

2

CRDC2 Y Centroid

Figure 4.5: Drift correction for CRDC2 Y position. (Top left), Uncorrected Y distributionin CRDC2 as a function of Run Number. (Top right), Uncorrected centroids of CRDC2 Yposition as a function of Run Number. (Bottom left). Corrected Y distribution in CRDC2.(Bottom right) Centroids of corrected Y distribution in CRDC2 as a function of run number.

beam was used for this purpose since the 24O beam was not intense enough.

In order to ensure that each pad gives the same signal for the same amount of charge

collected it is necessary to gainmatch them. For this procedure, the incoming 20O beam

is selected to remove impurities. In addition, a gate is placed on a good response in the

CRDCs to remove events with strange trajectories. It is also assumed that the beam loses

a negligible amount of energy in the first half of the detector compared to the second half.

If we approximate the detector as 65 cm of pure Ar gas (ρ = 1.66 ∗ 10−3g/cm3), the total

energy loss for 20O at 118 MeV/u in the first half of the detector is 16 MeV, and 16.1 MeV

73

in the second half.

Charge (arb.) Pad 40 50 100 150 200 250

Co

un

ts

0

200

400

600

800

1000

1200

Charge (arb.) Pad 9 (Ref.)0 50 100 150 200 250

Co

un

ts

0

200

400

600

800

1000

1200

1400

Figure 4.6: Example of gaussian fitting procedure for gainmatching of the IC pads. Pad 4is shown on the left, and the reference pad, pad 9 on the right.

The gainmatching is performed by determining a slope for each pad:

qcal = mi ∗ qraw

Where qraw is the raw charge collected on each pad, and mi is the slope defined as:

mi = cref/ci

Here cref is the centroid of the reference pad, and ci is the centroid of the ith pad determined

by a gaussian fit. Example fits are shown in Fig. 4.6 for pad 4 and pad 9. Pad 9 was chosen

as the reference pad, as it is in the middle of the detector and displayed a signal that was

roughly in the middle of the variation from all other pads.

The results of the gainmatching procedure are shown in Fig. 4.7. It is apparent that pad

1 and 8 show abnormally low charge collection, and thus are excluded from analysis. For

74

the remaining good pads, the peaks line up and the widths are approximately the same.

Pad #0 2 4 6 8 10 12 14 16

Ch

arg

e (a

rb.)

0

50

100

150

200

250

300

Raw PadsRaw Pads

Pad #0 2 4 6 8 10 12 14 16

Ch

arg

e (a

rb.)

0

50

100

150

200

250

Gainmatched PadsGainmatched Pads

Figure 4.7: Results of applying the gainmatching calibration for the IC. Raw pads on shownon the left and calibrated pads on the right.

There is some variation in the charge collected in each pad as a function of the X position

due to inefficient charge collection. Each pad has a different position dependence, and so

each pad must be corrected independently to achieve the best resolution. To accomplish

this, a “sweep run” was used where the beam was swept back and forth across the focal

plane to illuminate the detector at different X-positions. Since magnetic fields do no work,

the beam has the same energy despite the varying sweeper setting and so the same amount

of charge is being deposited at each X position. Using 5 mm wide slices in X, the centroid of

the charge deposited on each pad is determined by a gaussian fit and plotted as a function

of the X position. The dependence is then fit with a polynomial of appropriate order and

removed by the following expression:

qpos =qcal∑aixi

where qcal is the gainmatched charge, and ai represent the polynomial coefficients.

75

X [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

50

100

150

200

250

Prob 0.02128

p0 0.5049± 114.1

p1 0.0101± ­0.01795

p2 0.0001747± ­0.0006744

p3 1.753e­06± ­1.079e­05

Prob 0.02128

p0 0.5049± 114.1

p1 0.0101± ­0.01795

p2 0.0001747± ­0.0006744

p3 1.753e­06± ­1.079e­05

PAD 15

X [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

50

100

150

200

250

Position Corrected

Figure 4.8: Example of position correction in the ion chamber for pad 15. The raw signalas a function of X position is shown in the left panel, with the best-fit super-imposed. Theright panel shows the result of the correction.

This method was only applied for the X position correction, as there was no noticeable Y-

dependence. After each pad has been gainmatched and position-corrected, the total energy

loss is determined by the sum of all pads:

Qtot =∑

qpos

The results for the position correction are shown for pad 15 as an example in Fig. 4.8.

The ion chamber exhibited a slow drift over the course of the experiment. This is shown

in Fig. 4.9 for the reaction products from the 24O beam. The drift was fit with the functional

form:

dE(t) = p0 +p1

t+ p2

76

The final drift-corrected energy loss then becomes:

dEcorr = Qtot/dE(t)

To determine the coefficients for the drift correction, a gate is placed on the selection of 24O

beam, good CRDCs, and on oxygen in the ion chamber (denoted by the red lines in Fig.

4.9). The coefficients for the drift correction are summarized in Table 4.3.

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

Ch

arg

e (a

rb.)

0

50

100

150

200

250

Uncorrected IC Sum

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

Ch

arg

e (a

rb.)

155.5

156

156.5

157

157.5

Charge Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

Ch

arg

e (a

rb.)

0

50

100

150

200

250

Corrected IC Sum

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

Ch

arg

e (a

rb.)

154.1

154.2

154.3

154.4

154.5

154.6

154.7

154.8

Charge Centroid

Figure 4.9: Drift correction for IC sum. (Top left), Uncorrected charge distribution in the ICas a function of Run Number. (Top right), Uncorrected centroids of the charge distributionas a function of Run Number. (Bottom left). Drift Corrected charge distribution in the IC.(Bottom right) Centroids of the drift corrected charge distribution.

77

Drift Correctionp0 154.8p1 210.9p2 -2971.2

Table 4.3: Drift correction parameters for the Ion Chamber.

4.1.1.3 Thin Scintillator

The thin scintillator is located after the ion chamber in the sweeper focal plane and provides

an additional measurement of the energy loss in addition to time-of-flight information. The

detector has four PMTs mounted on light-guides as illustrated in Fig. 3.8, and are labeled

0 through 3. The signal from each PMT gives a time and a charge measurement which are

combined to give a total energy loss and the interaction time. Due to inhomogeneities and

attenuation in the plastic, there is variation in the charge-collection efficiency for each PMT

based on the interaction position in the detector. Thus, each PMT needs to be gainmatched

and position corrected.

An 20O beam was sent down the center of the focal plane for gainmatching of the PMTs.

This ensured that the middle of the thin scintillator was illuminated and that the distance

from the interaction point to each PMT was roughly equal. The sweeper was set to I = 350A

with a central rigidity of Bρ0 = 3.767 Tm for this run. Due to the logistics of warming and

cooling the liquid deuterium target, it was more time-efficient to use a 670 mg/cm2 Be

degrader while the target was kept in a gaseous state (50 K) instead of waiting for the target

to liquefy. The choice of 670 mg/cm2 of beryllium was to mimic the expected energy-loss

through the deuterium target. In addition, a selection was made on oxygen isotopes in the

ion chamber, and each event was required to fall within a 20 mm x 20 mm square centered

on the thin scintillator. The position on the thin scintillator was determined by projection

78

from the CRDCs.

PMT # (arb.)0 0.5 1 1.5 2 2.5 3 3.5 4

(ar

b.)

iq

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Raw ChargeRaw Charge

PMT # (arb.)0 0.5 1 1.5 2 2.5 3 3.5 4

(ar

b.)

iq

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Calibrated Charge

Figure 4.10: Before (left) and after (right) the gainmatching of the PMTs in the thin scin-tillator.

The charge signals from each PMT are calculated in a similar manner to the ion chamber,

and gainmatched in the same way:

qcal = mi ∗ qraw + q0

Where the slope are determined by a ratio of gaussian widths with respect to a reference

PMT (PMT 0, see Fig. 3.8), and the offset is set to line up the peaks:

mi =σrefσi

Fig. 4.10 shows the charge collected in each PMT before and after gainmatching. Once

all four PMTS are gain-matched, their signals are combined to provide a measurement of

79

the total charge deposited in the plastic, which is defined as follows:

qtop =qLU + qRU

2

qbot =qLD + qRD

2

qtot =

√q2top + q2bot

2

Where qLU,LD,RU,RD are the gainmatched signals from the left-upper (lower) and right-

upper (lower) detectors respectively. The total charge signal qtot exhibited both a positional

dependence inherent in each PMT signal as well as an overall time dependence as the de-

tector drifted over the course of the experiment. These effects were corrected by using the

same method as the ion chamber. The position dependence was removed by a sixth-order

polynomial:

qposcorr =qtot∑aixi

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X [mm]­200 ­150 ­100 ­50 0 50 100 150 200

Ch

arg

e

400

450

500

550

600

650

700

750

800

RawRaw

X [mm]­200 ­150 ­100 ­50 0 50 100 150 200

Ch

arg

e

400

450

500

550

600

650

700

750

800

Position CorrectedPosition Corrected

Figure 4.11: Correction of the position dependence in the thin scintillator. (Left) the rawcharge signal as a function of X position with the best-fit superimposed. (Right) Result ofposition correction.

80

Position Correction Drift Correctiona0 651.7 p0 742.7a1 0.2001 p1 -43364

a2 -4.71*10−3 p2 -2374

a3 -2.31*10−5

a4 7.55*10−8

a5 3.08*10−10

a6 4.63*10−15

Table 4.4: Coefficients for position correction (left) and drift correction (right) of the Thinscintillator.

Figure 4.11 shows the energy-loss in the thin scintillator as a function of the X position

determined by the CRDCs. To map out this dependence, a “sweep run” was used as described

in previous sections. No significant Y dependence was observed, and thus was not corrected.

The detector drift was handled the same way as the ion-chamber:

dE(t)thin = p0 +p1

t+ p2

With the final energy signal being:

dEcorr = qtot/dE(t)thin

The drift-corrected energy signal can be seen in Fig. 4.12. The slight correlation is removed.

The coefficients for the position and energy-drift correction can be found in Table 4.4.

Only an offset is used to calibrate the timing signal of each PMT. The slope of the TDC is

assumed to be 0.1 ns/ch since the range of the TDC is fixed. In addition, there is about a 20

ns jitter introduced the Field Programmable Gate Array (FPGA) in the sweeper electronics.

Since the TDCs receive a start from the individual PMTS and the stop is generated by

the FPGA, the amount of jitter can vary event-by-event. However, the same stop signal is

81

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

Ch

arg

e (a

rb.)

0

200

400

600

800

1000

1200

1400

totUncorrected Thin q

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

Ch

arg

e (a

rb.)

678

680

682

684

686

688

690

Charge Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

Ch

arg

e (a

rb.)

0

200

400

600

800

1000

1200

1400

totCorrected Thin q

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

Ch

arg

e (a

rb.)

732.5

733

733.5

734

734.5

735

735.5

Charge Centroid

Figure 4.12: Drift correction for charge collection in the thin scintillator. (Top left), Uncor-rected charge distribution in the thin as a function of Run Number. (Top right), Uncorrectedcentroids of the charge distribution as a function of Run Number. (Bottom left). Drift Cor-rected charge distribution in the thin. (Bottom right) Centroids of the drift corrected chargedistribution.

used for all PMTs so the jitter is the same for each timing signal. The jitter is eliminated

by subtracting one timing signal from the remaining others after applying the slope of 0.1

ns/ch. In the past the reference signal has been Thin PMT0, however in this experiment

this signal would drop out intermittently and so a more stable copy of the signal passing

through different electronics was used, called “sweeper trigger”. This did not affect the qtot,

as the charge signal was always present.

The individual offsets for each PMT were determined using the same method as the

gainmatching. Events which hit the center of the detector were selected and the centroid

82

PMT Offset [ns]0 31.31 -24.02 -74.93 -5.94

Table 4.5: Time offsets for the Thin scintillator.

of each PMT was aligned with that of Thin PMT0. The overall offset for Thin PMT0 was

determined by the expected time-of-flight for the beam. For this calibration, the beam was

20O at 118 MeV/u impinging upon a 670 mg/cm2 Be degrader with a flight path of 417.86

cm from the target to the thin. This gives a calculated time-of-flight of t0 = 31.28 ns, and

determines the offset of Thin PMT, and hence the offset of the other PMTs. These offsets

are listed in Table 4.5. Once the offsets are determined, the calibrated timing signal for the

entire detector is formed from the average of each PMT:

tthin =1

n

n∑i=0

ti

Where n is the number of PMTs that fired for a given event and ti are the timing signals

of each PMT. The individual timing signals of each PMT drifted over the course of the

experiment with the worst case being about a 1 ns drift in timing. Because the trends for

each PMT are different they were corrected individually. Instead of a global function for the

drift, like in the case of the ion-chamber, the offsets for each PMT were varied run-by-run

to eliminate this drift. This was done by selecting a reference run, Run3030, and finding

the change in timing relative to the reference, δt = t − tref , and subtracting δt from the

observed time. A list of δt was then stored in a hash-table so that the calibration could be

performed run-by-run. Figure 4.13 shows the drift in the combined signal and the effect of

the correction. The gradual shift in timing is removed.

83

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[n

s]th

int

26

28

30

32

34

36

38

40

Uncorrected Thin Timing

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[n

s]th

int

31.2

31.3

31.4

31.5

Timing Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[n

s]th

int

26

28

30

32

34

36

38

40

Corrected Thin Timing

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[n

s]th

int

31.2

31.3

31.4

31.5

Timing Centroid

Figure 4.13: Drift correction for the timing of the thin scintillator. (Top-left) The averagetime tthin is shown as a function of run number. (Top-right) The centroid of the timingsignal as a function of run number. (Bottom-left) Drift corrected thin timing as a functionof run number. (Bottom-right) Corrected timing centroids using the offset method.

4.1.1.4 Target and A1900 Timing Scintillator

There are two other timing scintillators in the beam-line. The A1900 scintillator was placed

immediately after the A1900, and the target scintillator was placed 105.92 cm upstream from

the center of the LD2 target. The target scintillator has a single PMT attached to it that

records both time and charge. The A1900 scintillator was located 10.579 m upstream and

only the timing signal was recorded. Both TDCs for the scintillators have a fixed slope of

0.1 ns/ch, and their calibration follows the same method as the individual thin PMTs. After

the TDC channel is converted to ns, the FPGA jitter is subtracted. This leaves a global

84

A1900 and Target Scint. Offset [ns]A1900 -123.6Target 52.61

Table 4.6: Timing offsets for the Target and A1900 Scintillators.

offset to be determined. To find the offset, a “beam down center” run was used with the

an 20O beam and a 9Be degrader. The offsets are set so that the velocity of the unreacted

beam is properly reproduced between the two scintillators. They can be found in Table 4.6.

Both the target scintillator and the A1900 exhibited a gradual time dependence. This

is corrected in the same manner as the thin PMTs. A reference offset is chosen and a δt

calculated relative to that offset on a run-by-run basis. The calibrated time is then shifted

δt to remove the drift. The drift correction for the target scintillator is shown in Fig. 4.14,

and for the A1900 scintillator in Fig. 4.15.

4.1.1.5 Hodoscope

The CsI(Na) array, or Hodoscope, did not function properly during this experiment due

to a smoothing of the crystal surface, likely due to the formation of water droplets which

caused the teflon wrapping to come in contact with the crystal face. The detectors rely on

total internal reflection to direct the light produced from an event to a PMT at the end of

the CsI(Na) crystal. Normally the surface of the CsI is sanded so that the surface is rough

leaving gaps between it and the teflon covering. For total internal reflection to occur, the

interface of the crystal and the teflon must have a gap so that the when the light is incident

on the medium in between the crystal and its wrapping it is not transmitted. When the

angle of incidence exceeds a critical angle, the amplitude of the transmitted wave becomes

zero. The critical angle depends on the index of refraction of the materials:

85

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[n

s]ta

rget

t

­25

­20

­15

­10

­5

0

Uncorrected Target Timing

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[n

s]ta

rget

t

­14.4

­14.2

­14

­13.8

­13.6

­13.4

Timing Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[n

s]ta

rget

t

­25

­20

­15

­10

­5

0

Corrected Target Timing

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[n

s]ta

rget

t

­13

­12.8

­12.6

Timing Centroid

Figure 4.14: Drift correction for the timing of the target scintillator. (Top-left) The timingsignal is shown as a function of run number. (Top-right) The centroid of the timing signalas a function of run number. (Bottom-left) Drift corrected target scintillator timing as afunction of run number. (Bottom-right) Corrected timing centroids using the offset method.

sin(θc) = nmedium/nCsI

However, if the size of gap between the teflon and CsI becomes comparable to the wave-

length of the light, it can be transmitted through the teflon resulting in poor resolution.

CsI(Na) crystals are hydroscopic. If the crystals were exposed to a humid environment dur-

ing their manufacture then water droplets could have formed in between the teflon and the

surface of the crystal. The resulting condensation can cause the surface to become smooth

allowing teflon to stick to the crystal leading to light leaks.

86

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[n

s]A

1900

t

­150

­140

­130

­120

­110

­100

­90

­80

­70

Uncorrected A1900 Timing

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[n

s]A

1900

t

­111

­110.8

­110.6

­110.4

­110.2

­110

Timing Centroid

Run Number (arb.)3000 3020 3040 3060 3080 3100 3120 3140 3160 3180 3200

[n

s]A

1900

t

­150

­140

­130

­120

­110

­100

­90

­80

­70

Corrected A1900 Timing

Run Number (arb.)3040 3060 3080 3100 3120 3140 3160 3180

[n

s]A

1900

t

­110.05

­110

­109.95

Timing Centroid

Figure 4.15: Drift correction for the timing of the A1900 scintillator. (Top-left) The timingsignal is shown as a function of run number. (Top-right) The centroid of the timing signalas a function of run number. (Bottom-left) Drift corrected A1900 timing as a function ofrun number. (Bottom-right) Corrected timing centroids using the offset method.

A 20O beam was used to map-out the position dependence of the crystals. By sweeping

the beam back and forth the middle row (modules 10-14) of the hodoscope was illuminated.

The position on the crystal face can be determined with the CRDCs to ∼1 mm resolution.

Plotting the total charge collected on the z-axis and the X and Y position in the crystal on

the X and Y axis shows unique patterns for each crystal (Figure 4.16.)

It is evident that the signal quality is degraded in areas with low light collection, causing

the overal resolution of the array to be significantly worsened. Large portions of the crystals

are un-usable. Upon removing the middle-row after the experiment, an inspection confirmed

87

1700

1710

1720

1730

1740

1750

1760

1770

1780

1790

1800

[mm]relX­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

[m

m]

rel

Y

­50

­40

­30

­20

­10

0

10

20

30

40

50Module 10Module 10

2260

2280

2300

2320

2340

2360

2380

2400

2420

2440

[mm]relX­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

[m

m]

rel

Y

­50

­40

­30

­20

­10

0

10

20

30

40

50Module 11Module 11

1800

1850

1900

1950

2000

2050

2100

2150

[mm]relX­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

[m

m]

rel

Y

­50

­40

­30

­20

­10

0

10

20

30

40

50Module 12Module 12

1900

1950

2000

2050

2100

2150

2200

[mm]relX­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

[m

m]

rel

Y

­50

­40

­30

­20

­10

0

10

20

30

40

50Module 13Module 13

2160

2180

2200

2220

2240

2260

2280

2300

2320

2340

[mm]relX­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

[m

m]

rel

Y

­50

­40

­30

­20

­10

0

10

20

30

40

50Module 14Module 14

Figure 4.16: Light collection in the middle row of the Hodoscope for Run 3002 where an20O beam was swept across the focal plane. Ideal behaviour would be a uniform response.On the X and Y axis are the X and Y positions relative to each crystal, the color axis is thetotal energy deposited.

that the teflon was sticking to the surface. Due to a significant degradation of the hodoscope

resolution, this detector remains unused in this analysis.

4.1.2 LD2 Target

The Ursinus College Liquid Deuterium Target has two quantities that were monitored during

the experiment: pressure and temperature. It is important to monitor these quantities during

operation of the target to ensure the safety of the target as well track any fluctuations that

may occur. The pressure was monitored by a manometer in the gas-handling system that

provided a measurement of the target cell pressure. The manometer was controlled by a

MKS PDR 200 unit [97], which outputs a raw voltage signal with a resolution of 1 mV that

88

must be converted into a pressure. The temperature is monitored by a silicon diode which is

read-out by a Lake Shore Model 331S temperature controller that outputs an analog signal

with a resolution of < 1 mV. The uncertainty on this system is around ∼0.25 K according to

the manufacturer [98]. (The IEEE-488 analog interface has an accuracy of ± 2.5 mV, which

corresponds to 0.75 K. Factory settings for diodes are between 0.25 - 1 K uncertainty).

To calibrate the temperature and pressure of the cell, the raw signal is converted to

the appropriate quantity assuming the following functional forms (as recommended by the

manufacturers). For pressure the relation is:

P = p0 ∗ 102∗V [Torr]

And for temperature:

T = t0 ∗ V [K]

The coefficients p0 and t0 can be constrained simultaneously by fitting the phase-transition

of a particular gas. For this experiment, two types of gas were liquefied and data recorded

for the phase transition. A neon test gas was used to initially check the target system while

deuterium was used for the actual experiment. This provides a method of cross checking,

as a calibration to the phase transition of one gas must reproduce the phase transition of

the other. The phase transitions of neon and deuterium have been measured and can be

parameterized with the following forms.

For neon, data can be obtained from NIST [99, 100]:

log10(P ) = 3.75641− 95.599

T − 1.503

89

where the units for P are bar, and Kelvin for T . The vapor pressure for deuterium has also

been measured [101]:

log10(P ) = 5.8404− 70.044/T +4.59 ∗ 10−4

(T − 23)2

where P is in mm of Hg and T in Kelvin.

These parameterizations of the vapor pressure are only valid for a specific temperature

regime as they are an approximation. For the neon data this interval is from 15.9 - 27 K,

and for deuterium it is 14 - 24.5 K. The coefficients p0 and t0 can be determined by fitting

directly to a known phase-transition. Figure 4.17 shows the fit to the raw phase diagram for

D2 gas observed during liquefaction. From this calibration we see that the D2 gas did not

cross into a region where it would have frozen. The best fit parameters are:

p0 = 9.621 ∗ 10−6 [Torr]

t0 = 30.34 [K/V]

The calibration can be verified by applying it to the data the neon phase-transition, and

is shown in Fig. 4.18. The calibrated data are shown in black, while the NIST data are

shown in red. The dashed-lines give an error band. This is determined by systematically

shifting the temperature by the uncertainty reported in the neon measurement (δT = 0.5K

[100]) used to constrain the NIST parameterization. The data fall within the uncertainty of

the previous measurement confirming the calibration.

Once the temperature and pressure have been calibrated the target can be checked for

any drifts during its operation. Figures 4.19 shows the temperature and pressure over the

90

[V]rawT0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

[V

]ra

wP

3.96

3.98

4

4.02

4.04

[K]calT10 12 14 16 18 20 22 24 26 28 30

[to

rr]

cal

P

800

850

900

950

1000

1050

1100

1150

1200

1250

1300

Solid

Gas

Liquid

Figure 4.17: Temperature and Pressure calibration of the LD2 target. (Left) Raw voltagesfrom the EPICS readout from the temperature controller and manometer. The data are inblack, the region used to fit the phase transition is highlighted in red. (Right) Calibrationto phase-transition (blue line) in deuterium.

course of the experiment. The temperature fluctuation is less than 0.15 K which is well below

the uncertainty of the temperature controller. In addition, the pressure is very stable except

for a slow drop of about 5 Torr in the middle of the experiment. The pressure equalized for

the remaining duration and no further change was detectable. It is not likely a leak or a

failure of the target cell. Since this change is less than 1% of the pressure it is neglected.

It is crucial to determine the target thickness. Although the cell is designed to contain

200 mg/cm2 of LH2, the Kapton windows can deform under pressure causing the nominal

thickness of the target to increase. In addition, the heat-shield of the LD2 target was wrapped

in 5 µm of aluminized mylar to help keep the temperature stable, which adds aditional energy

loss, albeit small. The target thickness is determined by measuring the kinetic energy of the

unreacted 24O beam in the focal plane and determining the total energy loss. To measure the

kinetic energy of the unreacted beam, it is necessary to calibrate the CRDCs and perform

the inverse tracking. Details on those calibrations and the inverse tracking can be found in

sections 4.1.1.1 and 4.3.

91

[K]calT20 22 24 26 28 30 32 34 36 38 40

[to

rr]

cal

P

700

800

900

1000

1100

1200

1300

1400

Warm

ing

Cooling

Ph

ase

Tra

nsi

tio

n

Figure 4.18: Measured phase transition with a neon test gas using the calibration parametersfrom fitting the deuterium transition. The red line corresponds to data from Ref [100], andthe dashed lines are the uncertainty bands given a ±0.5K fluctuation. The red arrowsindicate data taken during initial cooling, liquefaction, and warming of the target. Theevents around 26 K and 1200 Torr are a result of a sensor error.

The incoming beam energy is known since the focusing quadrupole triplet before the

target was set to a Bρ of 4.03146 Tm thus giving an energy of Ebeam = 83.25 ± 1 MeV/u

for the 24O beam. A measurement on an empty cell gives a reconstructed beam energy of

Ebeam = 83.4 MeV/u, which agrees well with the triplet setting.

The kinetic energy of the unreacted 24O is shown after the inverse reconstruction in Fig.

4.20. The peak of the distribution is at E0 = 66.4 MeV/u giving a total energy loss of

Eloss = 17.1 MeV/u. The target thickness can be determined by estimating the energy

92

0

10

20

30

40

50

60

70

80

t [hrs]60 80 100 120 140 160 180 200

T [

K]

19.9

19.95

20

20.05

00:0

0 3

/30/

14

3/21

/14

3/22

/14

3/23

/14

3/24

/14

3/25

/14

0

10

20

30

40

50

60

70

t [hrs]60 80 100 120 140 160 180 200

P [

torr

]

840

845

850

855

860

865

00:0

03/

20/1

4

3/21

/14

3/22

/14

3/23

/14

3/24

/14

3/25

/14

Figure 4.19: Temperature and Pressure fluctuations over the course of the experiment start-ing from 4:00 AM 3/19/14. Time is measured in hours.

loss with LISE++ [102]. However, this requires knowing the density of liquid deuterium

which changes with the temperature. A parametrization of the density as a function of the

temperature can be found from data taken at NIST [103]:

ρ(T ) = 0.1596 + 3.395 ∗ 10−3T − 1.4086 ∗ 10−4T 2

93

Given the observed temperature fluctuations, the average density is ρ = 0.1712 g/cm3

with an uncertainty of about ±1.4∗10−3 g/cm3. This results in an uncertainty in the target

thickness of about 10 mg/cm2, corresponding to about 0.2 MeV/u in the energy loss of the

beam. At this density, the nominal thickness of the target is 514 mg/cm2.

[MeV/u]fragE58 60 62 64 66 68 70 72 74

Co

un

ts

0

500

1000

1500

2000

2500

3000

3500

= 66.4 [MeV/u]µ

= 1.9 [MeV/u]σ

Figure 4.20: Measured kinetic energy of the 24O beam after passing through the full LD2target.

Using a density of ρ = 0.1712 g/cm3 for LD2, the resulting energy after passing through

the mylar, kapton, and deuterium can be calculated and compared to experiment. The

target thickness was determined to be t = 630+45−40 mg/cm2, where the error arises from

the uncertainty in the beam energy (σbeam = 1MeV/u). This is significantly larger than

the nominal thickness. Repeating this process with the 27Ne contaminant beam yields a

thickness of t = 650 ± 30 mg/cm2. There is approximately a 40 mg/cm2 uncertainty from

the beam energy, 5 mg/cm2 systematic uncertainty in the choice of beam, and 10 mg/cm2

due to the density fluctuation of the target, giving a combined thickness of t = 640 ± 45

94

mg/cm2.

Additionally, this uncertainty in the target thickness results in approximately a 0.5 − 1

MeV/u uncertainty in the energy loss which ultimately broadens any decay energy measure-

ment.

Figure 4.21: A 3.4 mm bulge in the LD2 drawn to scale.

The excess thickness of the target is a result of the bulging of the Kapton windows. To

account for the observed thickness, this bulge would have to be approximately b = 3.4 mm

which is roughly 10% the length of the target cell. Figure 4.21 shows a diagram of the bulge

drawn to scale. The size of the bulge can be estimated using an empirical result derived

for clamped windows. From the BNL OSHA safety guide (June 7, 1999) “Glass and plastic

window design for pressure vessels,” [104], the bulge b can be expressed in terms of the

pressure gradient ∆P , the Young’s Modulus of Kapton, E, the window thickness t = 125

µm, and window diameter (d = 38 mm):

∆Pd4

Et4= K1 ∗

(b

t

)+K2 ∗

(b

t

)3

The constants K1 and K2 are derived for windows which are clamped along their edge, and

are K1 = 23 and K2 = 55 respectively. Using the measured 850 Torr pressure differential

gives a value of b = 2.5mm which is less than the bulge needed to explain the observed

95

thickness, however this expression is only an estimate.

4.1.3 MoNA-LISA

The raw output from the PMTs in MoNA and LISA provide a charge and a time measure-

ment that reflects the total light collected by the PMT and the time of its arrival. Several

calibrations are needed to convert these measurements into deposited charge, position, and

interaction time. First, each PMT must be gainmatched and the QDC channels calibrated.

Then the corresponding TDCs calibrated, and a conversion from time-difference to position

within a bar determined. Each bar must then be placed in time relative to the first bar

in each table. Finally each table is placed in time relative to the target. The majority of

calibrations can be done with cosmic rays. Cosmic data was taken both before and after the

experiment. Cosmic muons deposit roughly 2.05 MeV/cm [105] in each detector as they pass

through with a velocity close to the speed of light. Thus approximately 20 MeV electron-

equivalent (MeVee) of light is deposited into each bar. Because of the dependence of the

light yield in organic scintillators on the type of particle, the MeVee is used to quantify the

absolute amount of light produced. 1 MeVee is defined as the amount of light produced by

an electron with 1 MeV of kinetic energy. Since the speed of the muons is close to c they

can be used to determine the relative timing of the bars.

4.1.3.1 Charge Calibration (QDC)

Each PMT was gainmatched by changing the voltages until the peak from cosmic muons

appeared in roughly the same channel for all PMTs. This process was repeated until the

cosmic peak was at roughly channel 900, and until the individual fluctuations in a PMTs

voltage were below 10 V. Typical voltages range from 1300-1950 V in MoNA and LISA.

96

QDC Channel0 500 1000 1500 2000 2500 3000

Co

un

ts

1

10

210

310

410

510

[MeVee]cal

q0 10 20 30 40 50 60 70 80 90 100

Co

un

ts

1

10

210

310

410

510

Figure 4.22: Example spectra used for QDC calibration in MoNA-LISA. (Left.) Raw QDCchannels for data taken with cosmic rays. The red curve is a gaussian fit to the cosmic-raypeak. (Right) Pedestal subtracted and calibrated charge spectrum. The cosmic ray peakappears around 20-30 MeVee.

The QDC calibration is done by taking cosmic data after having gainmatched all PMTs

and determining a linear relation between raw channels and MeVee by finding the pedestal

peak and the cosmic peak:

qcal = (qraw − qped) ∗mq

Where mq is the QDC slope in MeVee/ch and qraw is the raw QDC channel and qped the

pedestal (ch). A threshold is placed above the pedestal, determined by:

Qthresh = qped/16 + 2

The slope is given by the difference between the cosmic peak and the pedestal. The factor

of 16 is necessary to convert the pedestal channel from 12 bits to 8 bits, as the pedestal and

threshold are stored as 12 and 8 bit numbers respectively. The 2 assures that the threshold

is placed above the pedestal.

97

TDC Channel0 500 1000 1500 2000 2500 3000 3500 4000

Co

un

ts

1

10

210

310

[ns]r ­ tl

t­20 ­15 ­10 ­5 0 5 10 15 20

Co

un

ts

0

50

100

150

200

250

300

[cm]A0x­150 ­100 ­50 0 50 100 150

Co

un

ts

0

20

40

60

80

100

120

140

160

180

Figure 4.23: TDC and X-position calibration spectra. (Left) Raw TDC channels for a runtaken with a time calibrator with a fixed interval of 40 ns, this determines the TDC slope.(Middle) Raw time-difference spectrum used to calculate the X-position. The red linesindicate the physical ends of the bar. (Right) Conversion of time-difference into X-position.Data taken with cosmics which fully illuminate the array.

This process is automated with a procedure that finds the location of the pedestal and

cosmic peak via gaussian fitting. An example fit is shown in Figure 4.22.

4.1.3.2 Position Calibration (TDC)

MoNA and LISA use time-to-digital converters (TDCs) to measure timing differences of

events within the array. When a TDC channel receives a pulse from the anode of a PMT

it begins charging a capacitor until it receives a delayed stop signal from the logic of the

electronics. The amount of charge on the capacitor corresponds to the time the TDC was

charging. There is slight variation in the capacitors of each TDC and so a slope must be

determined for each TDC. This is done by pulsing the system with an Ortec NIM Time

Calibrator module (Model 462), which provides pulses at specific intervals to the TDCs. For

this experiment, the pulse rate was set to 40 ns intervals and the TDC range was 350 ns.

Figure 4.23 shows an example TDC spectra for this calibration. The “picket-fence” is spaced

in 40 ns intervals, and can be used to calculate a slope for the TDC. A slope is determined

for every TDC channel in MonA and LISA. They are typically around 0.09 ns/ch.

Once the slope of each TDC is calibrated, the time differences between the left and right

98

PMTs of a bar can be used to determine the position of an event. Using cosmic rays, the full

length of each MoNA/LISA bar was illuminated and spectra of left-right time differences

were generated. A fermi-function is used to find the edge of each bar, from which the

time-difference is converted to a position via a linear relationship. Figure 4.23 shows an

example raw bar-position in a LISA and the corresponding calibrated position. The slope is

determined by the edge of the time-difference, and the offset is such that the bar is centered

in its own reference frame.

4.1.3.3 Time calibration (tmean + global)

It is important to know the relative timing between each detector in the array, so that the

neutron time-of-flight can be accurately determined. While the time of an event is determined

by the average of the PMTs, a timing offset needs to be determined to place each bar relative

to a reference bar. Finally, the reference bar needs an absolute offset to place it relative to

the target. The timing offset between bars is determined using cosmic ray data, while γ-rays

from the target are used to determine the offset relative to the target. The known velocity of

cosmic-ray muons can be used to determine the timing between events which pass through

all 16 bars in a layer, either vertically or diagonally. Only events which triggered a majority

of the bars in a layer and deposited approximately 20 MeV in each bar were used.

Except for the first layer, the top bar of each layer is used as a reference and each

subsequent bar in a given layer is placed relative in time to the top bar. For events which

pass vertically through the array the travel time is:

t =d

vµ

99

Where d the distance between interactions, and vµ = 29.8 cm/ns is the speed of the muon.

The difference between the expected and observed time determines the offset. Once each

vertical layer is placed in time, the layers themselves need to be placed relative to the bottom

bar of the front layer in each “table”. This is done using diagonal tracks which travel from

the top of each layer to the bottom bar of the front layer. Figure 4.24 illustrated the muon

tracks used to perform this calibration.

z x

y

x z

y

µ−µ−

J0

K15

Figure 4.24: Schematic of a cosmic ray tracks used to determine the relative offsets betweeneach bar. Offsets within a table are with respect to the bottom bar in the front layer. J0and K15 are example bars in the first and second layer of LISA.

Once each table (1 for MoNA, 2 for LISA) is placed in time relative to the bottom bar

of the front layer, a final offset must be determined to place that bar with respect to the

target. To accomplish this, γ-rays emitted from interactions in the target are used since

their velocity is well-defined and the positions of the bars are well-known. The offset is set

such that the reconstructed speed of the γ-rays is the speed of light.

Due to the low beam rate (< 200 pps), the entire set of production data was necessary

in order to gain enough statistics. In addition, a gate was placed on 22O fragments coming

from the 24O beam because the unreacted 24O produces a large background when it stops at

100

LISA (Θ = 0) LISA (Θ = 22) MoNA [ns]411.66 410.53 434.54

Table 4.7: Global tmean offset in nanoseconds for each table in MoNA-LISA.

the end of the sweeper focal plane. Fig. 4.25 shows the results of the calibration, the γ-ray

peaks show up at 29.97 cm/ns for each table. Table 4.7 lists the final time offsets for MoNA

and LISA.

[cm/ns]γv20 22 24 26 28 30 32 34 36 38 40

Co

un

ts

0

2

4

6

8

10

12

14

16

18

20

= 0 [deg]ΘLISA

[cm/ns]γv20 22 24 26 28 30 32 34 36 38 40

Co

un

ts

0

2

4

6

8

10

12

14

16

18

20

= 22 [deg]ΘLISA

[cm/ns]γv20 22 24 26 28 30 32 34 36 38 40

Co

un

ts

0

2

4

6

8

10

12

14

16

18

20

MoNA

Figure 4.25: Reconstructed velocity of γ-rays coming from the target in coincidence with22O fragments. The global timing offset is varied for each table to align the centroids atv = 29.97 cm/ns.

4.2 Event Selection

This section details how the data are reduced to the physics events of interest. Over the

course of the experiment, there are many events that are recorded that are unrelated to the

physical process one may wish to study. This may include background, contaminant beam,

or events that do not create a big enough signal to be useful and are of poor quality. For

example, some of the CRDC or ion chamber pads malfunctioned and produced data that

are not useful. The physical processes of interest are 24O(d,d’)24O∗ →22O + 2n and 24O(-

1p)23N→22N + 1n, which require selection of the beam and reaction products in coincidence

101

with neutrons.

4.2.1 Beam Selection

The coupled cyclotrons provided an 24O beam with 32% purity at an intensity of 0.6 pps/pnA

at 83±1 MeV/u, with the major contaminant being 27Ne. There are however a significant

amount of contaminants created in the wedge of the A1900. The magnet before the target

was set to a central rigidity of Bρ = 4.03146 Tm corresponding to a beam velocity of 11.89

cm/ns. Ideally, to identify the beam components, one would send the beam into the focal

plane without a target. However due to the nature of the setup of the Liquid Hydrogen

Target, it was impossible to have a data set with no material in the beam-pipe. The closest

approximation that could be achieved was to warm the target to 50 K where it would be in

a gaseous less-dense state and send the beam through the foils, which cause an energy loss

of around 1 MeV/u. Using a warm-target run, the beam was sent into the focal plane and

element identification was achieved by looking at dE vs. ToFtarget→thin.

One can remove the wedge fragments by correlating the time-of-flight from the end of

the A1900 to the target with the time difference between the RF signal from the cyclotrons

and the A1900. Fragments with the same Bρ, but different Z and A will have different

velocities, and so separation can be achieved. Here, the RF signal from the K1200 cyclotron

is used. The selection of 24O is shown in Figure 4.26, along with the Z identification of the

beam-components in the ion chamber.

102

1

10

210

310

[ns] A1900→RF ToF200 205 210 215 220 225 230 235 240 245 250

[n

s] t

arg

et→

A19

00

To

F

70

75

80

85

90

95

100

105

110

O24F

N

Ne27

Light Fragments

1

10

210

310

[ns] thin→target ToF30 32 34 36 38 40 42 44 46 48 50

dE

[ar

b.]

0

50

100

150

200

250

300

F

O

N

C

B

Be

Figure 4.26: (Left) Separation of the 24O beam by time-of-flight from the other beam contam-inates. (Right) Energy loss vs. time-of-flight spectrum for all beams and reaction products.Lines are drawn to guide the eye for each element.

4.2.2 Event Quality Gates

To separate isotopes and reconstruct their energies and momenta, it is necessary to have

accurate position information in the CRDCs. Occasionally the CRDCs failed to collect all the

charge deposited by an event resulting in an unreliable position determination. These events

can be removed by applying quality gates to the CRDCs, as events that have a pathological

charge distribution will give an unreliable position. These events can be identified by looking

at the σ of the gaussian fitting algorithm for the X position as a function of the padsum –

or integrated total charge. The CRDC quality gates for CRDC1 and CRDC2 are shown in

Figure 4.27. An additional quality gate is made between the CRDCs. There are some events

that deposit low charge in one detector, but high charge in the other. The tracking of these

events can be unreliable. A gate is placed around events that behave linearly in the charge

deposition between the two detectors. This cut is shown in Figure 4.28.

Since the Y-position in the CRDCs is determined by a time difference between an inter-

action in the thin scintillator and the collection of charge carriers in the anode of the CRDC,

there are some events where the charge carriers were unable to be fully collected resulting

103

0

5

10

15

20

25

30

35

40

45

Total Charge (arb.)0 2000 4000 6000 8000 10000

(p

ad #

)σ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

CRDC 1

0

5

10

15

20

25

30

Total Charge (arb.)0 2000 4000 6000 8000 10000

(p

ad #

)σ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

CRDC 2

Figure 4.27: σ vs. total integrated charge in the CRDCs. Quality gates are drawn in red.

in a poor determination of the Y-position. These events are removed by requiring a valid

Y-position in the calibration algorithm.

0

5

10

15

20

25

Total Charge (arb.)0 2000 4000 6000 8000

To

tal C

har

ge

(arb

.)

0

2000

4000

6000

8000

Figure 4.28: Total integrated charge of CRDC1 (Y-axis) vs. CRDC2 (X-axis). A gate,shown in red, is drawn around events that deposite a similar charge in both detectors. Agate is applied to select the 24O beam.

Additional cuts are made on proper charge collection in the PMTs of all timing scintilla-

tors. A good signal is required in the RF, A1900, target scintillator, and the thin scintillator.

This ensures that the events of interest have a good signal throughout the entire system.

104

4.2.3 Element and Isotope Identification

Several reaction products were expected from the 24O beam on the LD2 target. The sweeper

was set to a central Bρ = 3.524 Tm (320 A), corresponding to the expected energy of (d,p)

reaction products. The acceptance of the sweeper is approximately ±8% in rigidity, and so

only a fraction of the isotopes produced made it into the focal plane. For this experiment,

the reaction products include 22−24O, 18−22N, 16−18C, 13−15B, and 10−12Be.

Element separation is achieved by the correlation between the energy loss dE in the ion

chamber and the time-of-flight from the target to the thin scintillator. The Bethe-Bloch

relation gives the energy loss as a function of several parameters, including the density of

the material, mean excitation potential, but most importantly the charge Z and the velocity

β:

−dEdx∝ Z2

β2∗ f(β)

The full explicit formula can be found in Ref. [91] (pg. 31). Element separation can

be achieved by plotting the energy loss as a function β, or the time-of-flight. A dE − E

measurement could not be cleanly made due to poor resolution of the hodoscope. Figure

4.29 shows the element idenfication for products from the 24O beam.

The next step is isotope separation. Ideally, a dipole magnet will separate isotopes by

their rigidity. Given a set of isotopes with the same Bρ, their velocity can be written as:

v =∆L

∆t=Bρq

m=

Bρq

Amu∝ 1

A

Where q is the charge, L the flight path and t the time-of-flight. Thus the time-of-flight and

mass are proportional.

105

[ns] thin→target ToF38 40 42 44 46 48 50

dE

(ar

b.)

0

50

100

150

200

250

1

10

210

O

N

CB

BeLi

Figure 4.29: dE vs. ToF for reaction products coming from the 24O beam. Coincidencewith a neutron is not required.

In practice however, the distributions are broad which makes separation difficult since

there is variation in both L and the Bρ. This variation arises from several factors including

the emittance of the beam, straggling within the target, the nuclear dynamics of the reaction,

and the momentum kick from neutron evaporation.

The energy resolution of the hodoscope or the thin scintillator is not sufficient to separate

isotopes. However, the rigidity and L of the charged particles are related to their emittance in

the sweeper focal plane. To fully untangle the isotopes, it is necessary examine the correlation

between the time-of-flight, dispersive angle and position. The convolution between these

parameters is most clear for the lightest isotopes and can be seen when plotted in 3D as in

Figure 4.30.

106

[mrad]xθ

Dispersive Angle

­100­50

050

100

Dispersive Position [mm] ­100­50

050

100

[n

s] t

hin

→ta

rget

T

oF

40

45

50

55

Figure 4.30: 3D correlations for dispersive position, angle, and time-of-flight showing isotopeseparation for the carbon isotopes.

To untangle this correlation, a projection onto the dispersive angle and position axes is

made for a given ToF slice. Contours of iso-time-of-flight are then fit to a quadratic form:

f(x) = a2 ∗ x2 + a1 ∗ x+ a0

An example of this contour is shown in Fig. 4.31 for the oxygen isotopes. From this

quadratic expression a parameter describing both position and angle for constant ToF is

constructed:

t(x, θx) = θx − f(x)

Plotting this parameter against the time-of-flight shows isotope separation (Fig. 4.31).

A rotation will give a 1-dimensional parameter to cut on for isotope separation. This is

accomplished by a linear fit to one of the isotopes:

107

tcorr = ttarget→thin +m0 ∗ t(x, θx)

In addition, the large gap of the sweeper creates some dependence on the y-position and

y angle. Although it is in the non-dispersive direction, the sweeper field is not completely

uniform. The correction can also be taken to higher orders than quadratic making the more

general form:

tcorr = m−10 ∗ ttarget→thin + t(x, θx, y, θy, ...)

Where the function t(x, tx, y, ty, ...) is a linear combination of all the terms listed in Table

4.8 with their respective coefficients. While this method provides a corrected time-of-flight

for isotope separation, it does not identify the mass. A simple way to determine the mass of

the oxygen isotopes is to identify the beam spot, however this luxury does not exist for the

other isotopes. Re-examining the Bethe relation and assuming non-relativistic kinematics as

well as a constant Bρ:

∆E ∝ Z2

v2

Recall that Bρ = p/q = mv/Z, thus v2 = Z2(Bρ2)/m2. Substituting this into the Bethe

relation we obtain:

∆E ∝ Z2

v2=

Z2

Z2(Bρ)2m2 ∝ m2

Hence ∆E ∝ A2. In addition, the time-of-flight is inverse proportional to the velocity thus:

ToF ∝ A

Z

108

Dispersive Position x [mm]­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

[m

rad

]x

θD

isp

ersi

ve A

ng

le

­100

­80

­60

­40

­20

0

20

40

60

80

100

42

43

44

45

46

47

48

[ns] thin→target ToF42 43 44 45 46 47 48

f(x)

(ar

b.)

­200

­190

­180

­170

­160

­150

­140

­130

­120

­110

­100

0

10

20

30

40

50

60

70

80

Figure 4.31: Projection of Fig. 4.30 onto the 2D plane of ToF vs. dispersive position for theoxygen isotopes. The contour of iso-time-of-flight is shown in black. This correlation, whenplotted against the time-of-flight shows separation for the oxygen isotopes (Right), and canbe rotated in this plane for the purposes of making a 1D gate.

109

Parameter Coefficientttarget→thin 7.8231

x -0.5871

x2 −1.7182 ∗ 10−3θx 0.98959

θ2x 6.1376 ∗ 10−4

θ3x −1.51604 ∗ 10−5

y 6.04954 ∗ 10−2

y2 5.44903 ∗ 10−3

Table 4.8: Time-of-flight correction coefficients for isotope separation.

A plot of ∆E vs. ToFcorr, should then produce a matrix where each nucleus is uniquely

identified since A and Z are discrete. Figure 4.32 shows how nuclei fall in this matrix for

various combinations of A and Z (some fictional), with the only constraint being Z ≤ A.

What is important to notice, is that for integer values of A/Z, different elements fall

directly above one-another in a vertical line. Making a plot of ∆E vs. ToFcorr shows

this behaviour and the isotopes are easily identified. Immediately below the beamspot with

the same A/Z = 3 is 21N, making the heaviest nitrogen isotope in the acceptance 22N.

Continuing along, we see that other heaviest elements are 18C, 15B, and 12Be. A neutron

coincidence gate is required in MoNA to reduce the background caused by the unreacted

beam. No unbound states in the lithium isotopes can be seen as the statistics are too low.

The only lithium isotope in acceptance is 9Li, however there are no neutrons in coincidence

with this fragment.

The one-dimensional projections for isotope separation are shown in Figure 4.34 and

Figure 4.35 for oxygen and nitrogen respectively. A line is drawn where the gate for the

selection of 22O and 22N is placed.

110

Figure 4.32: Matrix of A2 vs. A/Z with the condition that Z ≤ A up to mass ∼ 25. Eachpoint is a separate nucleus (some unphysical).The red lines indicate curves of constant Z.

0

20

40

60

80

100

120

140

Corrected ToF (arb.)300 310 320 330 340 350 360 370 380 390 400

dE

(ar

b.)

0

20

40

60

80

100

120

140

160

180

200

Figure 4.33: Energy loss dE in the ion chamber vs. Corrected time-of-flight showing isotopeseparation. A coincidence gate with a neutron is required to reduced background fromunreacted beam. A vertical line at A/Z = 3 is drawn to guide the eye.

111

Corrected ToF [arb.]310 320 330 340 350 360 370 380

Co

un

ts

0

200

400

600

800

1000

1200O22

O23 O24

Figure 4.34: One-dimensional particle identification for the Oxygen isotopes. A gate is drawnat the vertical line to select 22O. Neutron coincidence with MoNA-LISA is required to reducethe background from unreacted beam.

Corrected ToF [arb.]300 310 320 330 340 350 360 370 380 390 400

Co

un

ts

0

50

100

150

200

250

300

350

N19

N20

N21

N22

Figure 4.35: One-dimensional particle identification for the Nitrogen isotopes. A gate isdrawn at the vertical line to select 22N. Neutron coincidence with MoNA-LISA is requiredto identify candidates for reconstruction.

112

4.2.4 Neutron Selection

MoNA-LISA is designed to detect neutrons, but it is also sensitive to background radiation

and other events which can cause scintillation. The primary source of background are cosmic

muons and γ-rays produced either from the target or in the surrounding environment. Events

that correspond to a neutron need to be correctly identified. To ensure that the analysis is

being performed on an event which is most likely to be a prompt neutron, each event within

the array is time-sorted.

Figure 4.36 shows the neutron time-of-flight in coincidence with 22O in the sweeper. Fig

4.37 shows the correlation between time-of-flight and total charge-deposited. Two peaks are

visible in the time of flight spectrum. This is due to the separation of the MoNA-LISA

tables. The first peak is from the portion of LISA at 0 degrees (z = 7.5m), while the second

is from MoNA which is further back (z = 8.8m). This separation is only visible because

23O has an unbound resonance at a very low decay energy of Edecay = 45 keV [73, 68, 63].

The off-axis portion of LISA does not see any events from this decay because the “neutron

cone” from the decay of 23O does not intersect the detector. A low-energy decay like that in

23O is forward focused in the lab frame. The neutron velocity distribution is narrow enough

to distinguish the tables. Larger decays with Edecay ∼ 1 MeV will smear out the time-of-

flight distribution, due to a larger forward/backward kick in the center-of-mass frame of the

decaying nucleus.

Prompt γ-rays from the target can be seen distinctly at around 25 ns, each peak corre-

sponds to a table in MoNA/LISA. They are gated out by requiring the neutron time-of-flight

to be greater than 50 ns. An additional gate is placed at 150 ns, as events beyond this are

dominated by random background. Examining the charge-deposited can help improve the

113

ToF [ns]­50 0 50 100 150 200 250

Co

un

ts

0

200

400

600

800

1000

1200

1400

1600

1800

2000

ToF [ns]0 10 20 30 40 50

Co

un

ts

0

10

20

30

40

50

60

70

80

90

Figure 4.36: Neutron time-of-flight spectrum in MoNA-LISA with 22O coincidence. Thesplitting is due to the narrow resonance in 23O and the fact that the MoNA-LISA tables arephysically separated. The insert shows γ-rays coming from the target.

ToF [ns]­50 0 50 100 150 200 250

[M

eVee

]d

epQ

0

10

20

30

40

50

60

70

80

Figure 4.37: Neutron time-of-flight spectrum vs. Charge deposited in MoNA-LISA with 22Ocoincidence. γ-rays typically deposits < 5 MeVee, while real neutrons can deposit up to thebeam energy. No background from cosmic rays is evident.

event selection since the random background from γ-rays deposits little charge (< 5 MeVee).

A high threshold of 5 MeVee is used to exclude the vast majority of background events. In ad-

dition, a multiplicity, consisting of multiple events within MoNA-LISA above this threshold,

114

is constructed.

Cosmic rays will deposit around 20 MeVee of energy in the detector and would be un-

correlated in time with a fragment, thus their distribution would be uniform. No such band

is visible in the charge vs. ToF spectra for neutrons in coincidence with 22O or 22N, and so

this background is negligible.

4.2.4.1 Two-Neutron Selection

When constructing a three-body system, it is crucial to correctly identify events which

are true two-neutron events. The fact that MoNA-LISA does not distinguish between one

neutron scattering twice from two unique neutrons interacting independently introduces a

complication. From a pure-detection point of view, the two situations are identical. However,

there is a method for increasing the likelihood that the selection of a multiplicity 2 (and

greater) event will consist of true two-neutrons compared to a single neutron scattering

twice.

First, a high threshold is required on every hit in MoNA – the energy deposited must be

greater than 5 MeVee. This removes events that produce γ-rays from inelasticlly scattering

off carbon. For example, a single neutron could undergo a 12C(n,γ) reaction within a bar

and scatter out of the detector volume without interacting again. The residual γ-ray can

then be detected, and the event will have multiplicity 2 despite there only being one neutron

interaction.

Next, a “Causality Cut” is made. This is a cut on the relative velocity V12 and distance

D12 of the first two interactions in MoNA-LISA. This technique has been used to enhance

the two-neutron signal in several previous measurements of three-body states [26, 54, 63, 25,

106, 55, 107]. Figure 4.38 shows a simulation, for comparison, of a 1n decay and a 2n decay

115

[cm/ns]12V0 10 20 30 40 50 60 70 80 90 100

[cm

/ns]

12D

0

50

100

150

200

250

300

1n Simulation

[cm/ns]12V0 10 20 30 40 50 60 70 80 90 100

[cm

/ns]

12D

0

50

100

150

200

250

300

2n Simulation

Figure 4.38: Relative distance D12 and velocity V12 for 1n (Left) and 2n (Right) simulations.The selection for 2n events is shown in by the shaded blue region.

in the D12 vs V12 phase-space. Events which come from one neutron scattering twice occur

primarily in bands along short-distance and high relative velocity or large-distance and low

relative velocity.

By requiring a large relative distance D12 > 50 cm, events which have a clear spatial

separation are selected. When a neutron scatters it will lose energy and its relative velocity

will be less than that of a separate neutron at beam velocity. To remove these events, a cut

is placed on V12 > 12 cm/ns, which is the beam velocity.

4.3 Inverse Tracking

In order to measure a two- or three-body decay energy it is necessary to know the full 4-

vector of the recoiling fragment in addition to the neutron. The 4-vector of the neutron can

easily be obtained with knowledge of its time-of-flight and position:

βn =d

t

116

γn =1√

(1− β2)

from which the total energy and momentum can be obtained. In the case of the fragment

however, these quantities are not directly measured. Instead, the position and angle of

the fragment after exiting the sweeper are determined by the CRDCs and these variables

(xcrdc, θcrdcx , ycrdc, θcrdcy ) must be transformed into the target-frame. The energy is deter-

mined by the fragments deviation from the central path of the magnet, which has a known

rigidity. Once the energy is known, the momentum can be calculated, and the off-axis

components are determined by θTx and θTy :

px,y/p0 = sin(θx,y)

A full description of the technique is described in Ref. [108, 90], only a summary is

presented here. It is possible to calculate ion-optical quantities for a particle as it exits the

magnet:

xcrdc

θcrdcx

ycrdc

θcrdcy

∆L

= Mf

xT

θTx

yT

θTy

δ

where Mf is a forward transformation matrix. The variable ∆L is the difference between

the length the particle traversed, and the length of the central track which is defined as the

distance for which the particle is influenced by a magnetic field. This is close to the distance

from the target to CRDC1. The drift length L0 is the theoretical length a particle would

117

travel if it’s Bρ matched the sweeper exactly. The variable δ is the relative energy deviation

give by:

δ =E − E0

E0

Where E0 is given by the central track and the Bρ setting of the magnet. A hall probe

is placed inside the sweeper chamber to provide a measurement of the magnetic field. The

field of the dipole has been measured [90, 94], and the field-map is used as an input to the

ion-optics code COSY INFINITY [109].

The matrix Mf is useful if the incoming distribution of the beam is known. However,

the quantities that are measured experimentally are after the dipole. Thus it is necessary

to invert the matrix so that the CRDC variables can be used as an input to calculate the

appropriate quantities at the target:

θTx

yT

θTy

∆L

δ

= Mi

xcrdc

θcrdcx

ycrdc

θcrdcy

xT

However, to do a direct inversion of the matrix the quantity ∆L needs to be known a

priori. The approach taken by COSY is to calculate an inverse matrix Mi assuming that

the x-distribution of the beam is a delta function at x = 0 at the target. This allows for a

partial inversion of the matrix Mf and the calculation of (xT , θTx , yT , θTy ) and δ at the target

allowing the 4-vector of the fragment to be determined. The assumption of x = 0, will worsen

the resolution of the decay energy but it should not shift the peak of the distribution. If the

118

beam is not centered, then the reconstructed energy and x angle will also shift. The drift

length used for reconstruction was L0 = 1.56 m. The inverse reconstruction can be verified

by examining the neutron and fragment energies and angles, as well as by comparing to

previous measurement.

4.3.1 Verification

The inverse tracking can be verified by examining the reconstructed neutron and fragment

angles and energies. In addition, where possible, several unbound resonances can be com-

pared to previous experiments also performed with the MoNA - Sweeper setup.

4.3.1.1 22O + 1n

The inverse tracking is verified using the well-known low energy decay of 23O → 22O + 1n.

This resonance has been measured previously multiple times, and is known to be low-lying

at E = 45 keV. This is an ideal case to check the tracking, as MoNA-LISA has the highest

detection efficiency for decays < 100 keV and the full neutron-cone falls within the detectors

acceptance. In addition if the decay is reconstructed correctly, the inverse tracked angles of

the fragment will match the neutron angles. The centroids of the reconstructed fragment

energy and the neutron kinetic energy should also line up and finally, the relative velocity

vn − vf , must be symmetric about zero. These are shown in Figures 4.39 and 4.40, where

the neutron and fragment kinetic energy, relative velocity, and angles are compared. The

neutron and fragment distributions are shown in blue and black respectively.

As an additional check, the angular distribution of the fragment and the neutron-fragment

opening angle can be compared with a previous measurement of the same resonance using

the same experimental equipment with similar resolutions [73]. In that experiment 23O

119

KE [MeV/u]0 20 40 60 80 100 120 140 160 180 200

Co

un

ts

0

200

400

600

800

1000

1200 Neutron KE

Fragment KE

[cm/ns]relv­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5

Co

un

ts

0

500

1000

1500

2000

2500

3000

3500

Figure 4.39: Comparison of neutron (blue) and fragment (black) kinetic energy for the decayof 23O. The relative velocity is shown on the right.

Txθ

­200 ­150 ­100 ­50 0 50 100 150 200

Co

un

ts

0

200

400

600

800

1000

1200

Tyθ

­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

Co

un

ts

0

500

1000

1500

2000

2500

θNeutron

θFragment

Figure 4.40: Comparison of neutron (blue) and fragment (black) angles at the target. Thelarge binning in θTY is due to the discretization of the MoNA bars.

was populated via knockout from 26Ne and the low-lying state was observed. While the

experimental equipment is similar, there are some differences. For example, the addition of

more MoNA bars and their configuration as well as some adjustments in the Sweeper. The

width and overall shape of the distribution - which are determined by the decay - agree well.

The two-body decay energy for 22O + 1n is shown in Fig. 4.42.

120

Opening Angle (n­f) [deg]0 2 4 6 8 10

Co

un

ts

0

50

100

150

200

250

Fragment Angle [deg]0 1 2 3 4 5 6

Co

un

ts

0

20

40

60

80

100N. Frank (2008)

Current Exp.

Figure 4.41: Comparison of measured neutron-fragment opening angle θn−f and fragment

angle in spherical coordinates for the decay of 23O →22O + 1n. In black is the currentexperiment, shown in blue is a measurement of the same decay using the same experimentalapparatus [73] for comparison.

[MeV]decayE0 0.5 1 1.5 2 2.5 3 3.5

Co

un

ts

0

200

400

600

800

1000

1200

1400

1600

O + 1n22

Figure 4.42: 1n Edecay spectra for the decay of 23O. (Left) spectrum obtained from thecurrent experiment. (Right) A previous measurement performed on the same experimentalapparatus for comparison from Ref. [72]

4.3.1.2 21N + 1n

In addition to 23N, unbound states in 22N were also populated via 1p1n removal. Gating on

21N in the PID and reconstructing 22N shows a ∼ 600 keV peak in good agreement with a

previous observation by M.J. Strongman [110] shown in Fig. 4.43.

121

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

0

20

40

60

80

100

120

140

160

N + 1n21

Figure 4.43: Edecay spectrum for the decay of 22N → 21N + 1n. On the left is the spec-trum obtained from the current experiment. (Right) A previous measurement of the sameresonance also performed with MoNA [110].

4.3.1.3 23O + 1n

Unbound states in 24O were populated through inelastic scattering, (d,d’). Previous invariant-

mass measurements observed a 2+ state at 4.70 MeV, and a 1+ at 5.39 MeV, with decay

energies 0.51 and 1.2 MeV, respectively [70, 111].Shown for comparison in Figure 4.44 are

the results from this experiment, and those of Hoffman et al.[111] which was also measured

using MoNA. We are unable to resolve the two states because of the thick deuterium target.

Uncertainty in the reaction-point causes a broadening in the reconstruction which worsens

the resolution of the decay energy. In the work of Rogers et al. [70], it was shown that a

thinner target improved the resolution enough to separate the two states.

4.3.1.4 18C + 1n

Unbound states in 19C have also been previously measured with the MoNA - Sweeper setup,

[112] in addition to a RIKEN measurement [114]. A 76 keV resonance was observed in the

18C + 1n system. Figure 4.45. shows the results from this experiment compared to previous

122

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

0

10

20

30

40

50

60

70

O + 1n23

Figure 4.44: Edecay spectrum for the decay of 24O → 23O + 1n. (Left) spectrum obtainedfrom the current experiment. (Right) A previous measurement of the same resonances usingMoNA for comparison. [111]

[MeV]decayE0 0.5 1 1.5 2 2.5 3

Co

un

ts

0

20

40

60

80

100

120

140

Figure 4.45: (Top) Edecay spectrum for the decay of 19C → 18C + 1n obtained from thecurrent experiment. (Bottom) A previous measurement of the same resonance using MoNA[112, 113].

123

[112]. The low-lying resonance is apparent.

The inverse tracking in this experiment is able to reproduce decay energy spectra for at

least 4 different unbound systems measured on the same apparatus, giving confidence to the

calibrations.

4.4 Modeling and Simulation

Once the data have been calibrated and the spectra of interest generated, the parameters for

an observed resonance have to be extracted. This is done by comparison to simulation. An

in-house Monte Carlo simulation is used to generate simulated data that are convoluted with

the experimental resolution, acceptance and efficiency. The simulations take into account

the incoming beam profile, the geometry of the detectors – including the sweeper aperture,

as well as the efficiency of MoNA and LISA.

The simulation is divided into multiple steps. The input beam impinges a target of given

thickness and the reaction point is randomly chosen within the target. After determining

the appropriate energy loss, the reaction mechanism is simulated. In the case of neutron

emission, the neutron 4-vectors are determined at the reaction point and passed to GEANT

[115]. The remaining charged fragment passes through the rest of the target and through a

forward map of the magnet, which determines the distributions of positions at the CRDCs.

The CRDC distributions are then folded with their resolution.

The neutron 4-vector is passed to GEANT where interactions in MoNA and LISA are

modelled. Using MENATE R [116], the interaction cross sections for neutrons on carbon

and hydrogen are referenced to simulate the interactions in the plastic. In the cases where

the angular distribution of a reaction is known (e.g. elastic scattering), this distribution is

124

used in the center-of-mass frame. However, there are many inelastic processes for which the

angular distribution is not known and is assumed to be isotropic. The energy deposited from

the neutron interaction is determined by modeling the light collected in the PMTs, and the

time of the interaction is determined the same way as in the data.

In the case of multiple neutron simulations, GEANT handles the neutrons independently,

but the events are mixed afterward. In a two-neutron decay, the 4-vectors of both neutrons

are handled separately to determined the final number of interactions and their interaction

times. To make this comparable with data, the interactions from the neutrons are time-sorted

to give a single list of interactions that come from either neutron.

Once the interaction position of the neutron is determined and its time-of-flight calcu-

lated, the simulated data are taken and passed through the same analysis procedure as the

data. In other words, the outputs of the simulation are used as if they were data to construct

spectra that can be directly compared.

Various kinds of data are used to constrain simulation. Data taken on a gaseous target

is used to fix the beam energy while the beam profile and target thickness are constrained

by reproducing the unreacted beam in the focal plane. The reaction parameters are then

determined by examining the distribution of events in the CRDCs for a given reaction.

The simulation must reproduce the observed neutron kinetic energy, and reconstruct the

observed fragment energy. Finally, the decay energies and three-body correlations contrain

the resonance parameters.

4.4.1 Incoming Beam Parameters

The incoming beam parameters were set by matching the distribution of the unreacted

beam in the focal plane. In addition, they also had to match the inverse-reconstructed

125

distributions (θTX , θTY , y

T ) using an energy from the data on a gaseous target. The necessary

target thickness in simulation deviates slightly from what is observed. This is because

the simulation does not account for the Kapton and Mylar wrapping, or the curvature of

the target. Because of this, the thickness is varied in the simulation until the fragment

energy is properly reproduced. This ensures that fragments with the correct energy are

being transported through the model of the experimental setup. Thus the thickness in

the simulation is an effective thickness. A thickness of 650 mg/cm2 of LD2 matches the

incoming beam distributions very well 4.46. Table 4.9 summarizes the necessary incoming

beam distribution to reproduce the unreacted beam in the focal plane.

The A1900 momentum slits were set to 2% δp/p which resulted in an energy spread of

1.2%. Given that the magnetic quadrupole before the target was set to a Bρ = 4.03146 Tm,

this gives a beam energy for 24O of Ebeam = 83.4 ±1 MeV/u which is used in simulation.

4.4.2 Reaction Parameters

The 1p and 1n-knockout mechanisms were simulated by removing nucleons from the beam

and giving the resulting system a momentum kick in both the parallel and transverse direc-

tion. The parallel momentum kick was parameterized based on the Goldhaber [117] model

while the transverse kick was taken from Van Bibber’s model [118]. In these models, the

parallel and transverse kicks are gaussian and defined by widths σ⊥, and σ‖ which are free pa-

rameters. The widths are fixed by matching the distribution of fragments in the CRDCs for

a given reaction. An additional multiplicative factor is applied to slow the beam within the

target and is attributed to dissipative interactions within the target. Table 4.10 summarizes

the reactions and the parallel and transverse widths used to reproduce them.

126

Paramater Simulation Setting SignificanceeBeam 83.4 Beam enery in MeV/u.

dTarget 650 LD2 Thickness mg/cm2.bSpotCx 0 x centroid of incoming beam.bSpotCtx -0.01 θx centroid of incoming beam.bSpotCy 0.0 y centroid of incoming beam.bSpotCty -0.001 θy centroid of incoming beam.bSpotDx 0 width of x distribution.bSpotDy 0.002 width of y distribution.bSpotDtx 0.007 width of θx distribution.bSpotDty 0.008 width of θy distribution.bSpotCx2 0 x centroid, 2nd beam component.bSpotCtx2 0.005 θx centroid, 2nd beam component.bSpotCy2 0.003 y centroid, 2nd beam component.bSpotCty2 0.006 θy centroid, 2nd beam component.bSpotDx2 0.00 width of x distribution, 2nd component.bSpotDy2 0.01 width of y distribution, 2nd component.bSpotDtx2 0.005 width of θx distribution, 2nd component.bSpotDty2 0.008 width of θy distribution, 2nd component.normscale1 0.70 relative intensity of 1st component (70%).normscale2 1 relative intensity of 2nd component (30%).crdc1MaskLeft 0.15 +x edge of CRDC1 in m.crdc1MaskRight -0.15 −x edge of CRDC1 in m.crdc2MaskLeft 0.15 +x edge of CRDC2 in m.crdc2MaskRight -0.1305 −x edge of CRDC2 in m.crdc2MaskTop 0.15 top edge of CRDC2 in m.crdc2MaskBot -0.15 bottom edge of CRDC2 in m.crdc2dist 1.55 distance between CRDCs in m.cosymap ”m24O Jones320A” inverse and forward map filename.

Table 4.9: Simulation parameters for the incoming beam distribution. Determined by match-ing unreacted 24O in the focal plane.

Reaction σ⊥ (MeV/c) σ‖ (MeV/c) vshift24O(-1n)23O 92 64 0.987524O(-1p)23N 275 102 0.9550

Table 4.10: Parallel and perpendicular glauber kicks used to reproduce the CRDC distribu-tions.

127

X [mm]­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

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un

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0

200

400

600

800

1000

1200

1400

1600

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2000

CRDC1 XCRDC1 X

Y [mm]­150 ­100 ­50 0 50 100 150

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un

ts

0

500

1000

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2500

CRDC1 YCRDC1 Y

X [mm]­150 ­100 ­50 0 50 100 150

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un

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200

400

600

800

1000

1200

1400

CRDC2 XCRDC2 X

Y [mm]­150 ­100 ­50 0 50 100 150

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un

ts

0

200

400

600

800

1000

1200

1400

1600

1800

2000

CRDC2 YCRDC2 Y

[mrad]xθ

­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

Co

un

ts

0

500

1000

1500

2000

2500

CRDC1 TXCRDC1 TX

[mrad]yθ

­30 ­20 ­10 0 10 20 30

Co

un

ts

0

200

400

600

800

1000

1200

CRDC1 TYCRDC1 TY

Figure 4.46: Comparison between simulation (blue) and data (black) for the unreacted 24Obeam in the focal plane.

4.4.2.1 1n Knockout, Verification 22O

Using the incoming beam settings determined by the unreacted 24O beam setting, the parallel

and transverse kicks for modeling the 1n knockout reaction to 23O are constrained by data

128

[mrad]Txθ

­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

Co

un

ts

0

500

1000

1500

2000

2500

[mrad]Tyθ

­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

Co

un

ts

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

[mm]Ty­50 ­40 ­30 ­20 ­10 0 10 20 30 40 50

Co

un

ts

0

500

1000

1500

2000

2500

3000

3500

Figure 4.47: Reconstructed angles and target position using a 4-parameter map. The simu-lation (blue) is compared to data for the unreacted 24O beam (black).

KE [MeV/u]50 55 60 65 70 75 80 85 90

Co

un

ts

0

500

1000

1500

2000

2500

3000

O24Unreacted

Figure 4.48: Comparison of reconstructed kinetic energy distributions between simulation(blue) and data (black) for the unreacted 24O beam. The reconstructed energy is afterpassing through the full LD2 target.

with 22O in coincidence with neutrons as shown in Fig. 4.49. Settings for the beam can be

found in Table 4.9, and the reaction parameters in Table 4.10. In order to reproduce the

distributions in the CRDCs it was necessary to flip the sign on the incoming θx centroid,

indicating that the 22O fragments come in at a high angle. It is clear that the momentum

distribution of these fragments is not fully in acceptance.

129

X [mm]­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

Co

un

ts

0

200

400

600

800

1000

1200

CRDC1 X

Y [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

200

400

600

800

1000

1200

CRDC1 Y

X [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

200

400

600

800

1000

1200

CRDC2 X

Y [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

200

400

600

800

1000

CRDC2 Y

[mrad]xθ

­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

Co

un

ts

0

200

400

600

800

1000

1200

1400

1600

1800

CRDC1 TX

[mrad]yθ

­30 ­20 ­10 0 10 20 30

Co

un

ts

0

100

200

300

400

500

600

700

CRDC1 TY

Figure 4.49: Comparison of focal plane position and angles between simulation (blue) anddata (black) for 1n knockout to 23O, which then decays to 22O.

4.4.2.2 1p Knockout, Verification 22N

The data for 22N in coincidence with neutrons constrain the parameters for modeling 1p

knockout in the simulation. The CRDC distributions for this reaction are shown in Figure

130

KE [MeV/u]40 45 50 55 60 65 70 75 80 85 90

Co

un

ts

0

200

400

600

800

1000

1200

1400

1600

1800

O23O(­1n)24

Figure 4.50: Reconstructed kinetic energy for the 22O fragments coming from the 1n knock-out reaction. Simulation results are shown in blue and the data in black.

4.51. Settings for the beam can be found in Table 4.9 and the reaction parameters in Table

4.10.

4.4.2.3 (d,d’), Inelastic Excitation

The (d, d′) reaction can be approximated using the global optical models that are available.

The angular distribution for inelastic scattering of 24O on D2 was estimated using FRESCO

[119] and a global optical potential for 24O + d [120, 121]. As the deformation length is not

known, the deformation length for 12C was used. The differential cross section, dσ/dΩ, was

calculated for the 0+ → 2+ transition in 24O. The angular distribution was then randomly

sampled from in the simulation and the reaction kinematics treated as two-body kinematics.

The excited 24O then decayed, and the resulting reaction products propagated through the

rest of the simulation.

Since the three-body correlations and decay energies are relative measurements, the data

are not sensitive to the reaction mechanism. Identical spectra are produced whether or not

the reaction mechanism is modelled appropriately. There is no discernable difference between

131

X [mm]­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

Co

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ts

0

20

40

60

80

100

120

CRDC1 X

Y [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

20

40

60

80

100

120

CRDC1 Y

X [mm]­150 ­100 ­50 0 50 100 150

Co

un

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10

20

30

40

50

60

70

80

90

CRDC2 X

Y [mm]­150 ­100 ­50 0 50 100 150

Co

un

ts

0

20

40

60

80

100

120

CRDC2 Y

[mrad]xθ

­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

Co

un

ts

0

20

40

60

80

100

120

140

CRDC1 TX

[mrad]yθ

­30 ­20 ­10 0 10 20 30

Co

un

ts

0

10

20

30

40

50

60

70

80

90

CRDC1 TY

Figure 4.51: Comparison of focal plane position and angles between simulation (blue) anddata (black) for 1p knockout to 23N, which then decays to 22N.

using the FRESCO calculation or a glauber-kick without any stripping in the decay energies

and Jacobi spectra.

132

KE [MeV/u]50 55 60 65 70 75 80 85 90

Co

un

ts

0

20

40

60

80

100

120

140

160

180

200

N23O(­1p)24

Figure 4.52: Reconstructed kinetic energy for the 22N fragments coming from the protonknockout reaction. Simulation is in blue and data are in black.

[deg]CoMθ

0 20 40 60 80 100 120 140 160 180

[m

b/s

tr]

Ω/d

σd

­510

­410

­310

­210

­110

1

10

210

+ 2→ +O*(DWBA): 024

Figure 4.53: Center of mass angular distribution for inelastic scattering of 24O on d at 82.5MeV/u (lab), estimated with FRESCO, a global optical model, and the deformation lengthof 12C.

4.4.3 Neutron Interaction and MENATE R

The neutron interactions are modelled with GEANT [115] and the MENATE R package

[116]. MENATE R provides cross sections for interactions on hydrogen, carbon, iron, based

on previous measurements and the code’s ability to reproduce the neutron detection efficiency

for plastic scintillators. MENATE R contains several inelastic processes for neutrons on

133

carbon, for example 12C(n, np)11B, 12C(n,γ) in the energy range of 0 to 100 MeV. However,

data for these reactions is scarce and the angular distributions are not known and they are

crudely approximated in some cases. For example the 12C(n, γ) interaction is modelled with

the emission of only one γ-ray at 4 MeV, when in reality 12C can be excited beyond the first

excited state and emit a cascade. Figure 4.54 shows a summary of the inelastic processes

included in MENATE R.

[MeV]nT0 20 40 60 80 100

[b

]σ

0.1

0.2

0.3

0.4

0.5

0.6

0.7

12C(n,inl)*

[MeV]nT0 20 40 60 80 100

[b

]σ

0.1

0.2

0.3

0.4

0.5

0.6

0.7

12C(n,inl)*

12C(n,np)

12C(n,p)

)γ12C(n,

)α12C(n,3

12C(n,2n)

)α12C(n,

ENDF

Del Guerra (1970)

MENATE_R Sum

Figure 4.54: Breakdown of 12C(n,*) cross-section in MENATE R. (Left.) MENATE R crosssections without any adjustment. The blue curve is the sum of all cross-section in theenergy range 40 - 100 MeV. (Right) The total MENATE R cross-sections after modificationcompared to the Del Guerra compilation [122] and the ENDF [123] evaluation.

The 12C(n, np)11B cross section is overpredicted in the simulation. Summing the com-

ponents of each inelastic process, the total inelastic cross section is approximately 100 mb

too large compared to the 1976 compilation by Del Guerra [122], and the ENDF [123]

and JENDL-HE 2007 [124]databases. In addition, the only measurement of this reaction

at 90 MeV [125] reported this cross section as a factor 2 lower than what is included in

MENATE R. For this reason, this cross-section was modified in MENATE R to better agree

with the total inelastic cross section. Fig. 4.54.

The high threshold of 5 MeVee removes γ-rays that are produced by 12C(n, γ), which

are not appropriately modelled by MENATE R. The best agreement with MENATE R is

134

achieved when this threshold is applied.

4.4.4 Other Parameters

The field maps for the Sweeper magnet are fixed by measurement from a Hall probe inserted

in the field of the magnet. The geometric acceptances of the detectors are determined by

their geometrical layout in the simulation, which is identical to experiment. The steel vacuum

chamber of the magnet is included in the simulation. Resolutions for MoNA and LISA are

included as gaussian distributions and the quantization of the bars is also taken into account.

4.4.5 Cuts

Additional cuts were made to the simulation to remove tracks through the magnet that are

unphysical. These cuts were made to the emittance, shown in Figure 4.55. The physical

aperture of the CRDCs are included in the simulation but hard cuts are made on their

acceptance as a redundancy. In addition, the simulated neutrons are required to have physical

time-of-flights and be above the 5 MeVee threshold. Identical causality cuts are also made

to the simulation. In this way the simulations are made directly comparable to data.

4.4.6 Decay Models

4.4.6.1 One neutron decays

The decay energy for a single neutron decay is given by an energy-dependent Breit-Wigner

of the form (described in Section 2.1.1:

σl(E;E0,Γ0) ∝ Γl(E;E0)

[E0 − E + ∆(E; Γ0)]2 + 14 [Γl(E; Γ0)]2

135

CRDC1 X [mm]­100 ­80 ­60 ­40 ­20 0 20 40 60 80 100

[m

rad

]x

θC

RD

C1

­100

­80

­60

­40

­20

0

20

40

60

80

100

Figure 4.55: CRDC1 X vs. CRDC1 θX for all 22O fragments coincident with a neutron. Agate, called an XTX cut, is drawn around the data and applied to simulation. This is toreject fragments which may have a strange emittance in the simulation.

Where the normalization is arbitrary. This model is used to determine the neutron energy

and angular momentum ` relative to the fragment in the center-of-mass frame, and thus the

centroid E0 and width Γ0 of the unbound resonance. Both particles are then boosted back

into the lab frame in the simulation. This lineshape was used for modeling the 1n decay of

23O and 23N populated by neutron and proton knockout from 24O.

4.4.6.2 Two neutron decays

The decay of the excited state in 24O was modelled as a two-neutron decay to 22O. The decay

was modelled as multiple two-body decays using Volya’s description [77] for a sequential

decay. The intermediate state in 23O is well known and has been measured multiple times,

and the energy and width were fixed for the minimization. The total three-body energy was

determined by fitting the 22O + 2n spectra with causality cuts. The energy and width were

left as free parameters as well as the amplitude. The ` value is undetermined, as there was

no observable change in the lineshape between ` = 1, or ` = 2 once resolutions were folded

136

with the simulation. In addition, Volya’s model assumes that both neutrons decay with the

same ` value and come from the same single particle orbtial. Although this is not entirely

the case in the present decay, as discussed in Chapter 5, it is sufficient to describe the data.

Since the low-lying intermediate state in 23O decays by emission of a d5/2 neutron, the `

value was taken to be 2 for both decays.

For the phase-space model, the TGenPhaseSpace class was used as implemented in ROOT

[126]. This model uniformly samples the phase space of invariant mass of the fragment-

neutron and neutron-neutron pairs (M2f−n vs. M2

n−n) given the masses of each particle and

total n-body energy and width as an input. It is used as a baseline for the scenario with no

correlations since this model assumes no interaction.

For the di-neutron decay, the two neutrons are assumed to be in a 1S0 configuration

with a scattering length of a = −18.7 fm. In this model, the di-neutron cluster separates

from the core and then proceeds to break up with the a relative energy. The distribution

for the total three-body energy as well as the n− n relative energy is determined by Volya’s

di-neutron model described in Section 2.2.2. In both the di-neutron and sequential models,

the two-neutrons are emitted isotropically in the rest frame of the neutron - core/two-body-

subsystem. Additional details on two-neutron decays can be found in Section 2.2.

After folding with resolutions and acceptance, all experimental observables of interest are

modeled in the simulation under different assumptions and the best-fit values determined by

log-likelihood ratio described in the next section.

137

4.4.7 Fitting and Likelihood Ratio

For poisson errors, the log-likelihood function is written as:

L = −Ln [λ] = −∑i

Ln

(µnii e

−µi

ni!

)=∑i

Ln(ni!) + µi − niLn(µi)

Since we are only concerned with finding the set of µi generated by a hypothesis for which the

likelihood is maximum, the absolute magnitude is irrelevant. Thus we can add any constant

to this expression without affecting the minimization. Consider the likelihood of ni given

the expectation of ni:

−Ln [λ] = −∑i

Ln

(µnii e

−µi

ni!

)+∑i

Ln

(nnii e

−ni

ni!

)= −Ln

[λ(ni;µi)

λ(ni;ni)

]

Which is the likelihood ratio. This expression reduces to:

−Ln [λ] =∑i

µi − ni + niLn

(niµi

)

This quantity is distributed as χ2/2 in the limit of large n. In this case the null hypothesis H0

is the set of µi whose probability distribution is determined by theory (resonance parameters),

and the alternative hypothesis H1 is the set of data points ni under the assumption that

they too are sampled from a probability distribution (the “true” resonance parameters). The

data are assumed to be poisson distributed. Let θi denote the resonance parameters which

determine the probability distribution of µi. The minimization:

− ∂L∂θi

= 0

138

gives the parameters for which the likelihood is maximum (i.e. the “best-fit”).

Once the simulated distributions are made comparable to data by folding with reso-

lution, acceptances, and efficiencies, the log-likelihood ratio can be calculated for a given

set of energies and widths, or under different models (e.g. di-neutron, phase-space). Plot-

ting −Ln (λ) as a function of these parameters then defines the statistical boundaries via

rejection/acceptance within a critical region. In the case of χ2 this is often the p value.

In some cases it is useful to minimize on a linear combination of −Ln [λ] to better

constrain the simulation. For example, fitting on the sum of the mult ==1 and mult==2

gated spectra will force the model to reproduce the ratio of multiplicities whereas fitting on a

single spectrum alone can cause over-prediction of the other (and vice versa). The optimum

combination of spectra depends on the problem at hand and can vary depending on what

one wants to accomplish. In the case of multiple free parameters, the critical region can be

determined by:

θi ∈θ

∣∣∣∣ χ2 < χ2min + ∆χ2(ν)

Where ν is number of free parameters in the fit, and ∆χ2(ν) is the change in χ2 from

the minimum such that integration over the χ2 probability distribution function gives the

appropriate σ limits. Using Wilk’s Theorem, the statistic −Ln [λ] is distributed as χ2/2

in the limit of sample size N approaching infinity. For simplicity, one can approximate the

critical region for −Ln [λ] with the critical region of χ2/2, although Monte Carlo methods

will more accurately find this boundary.

139

Chapter 5

Results and Discussion

5.1 22O + 2n

The two- and three-body decay energy spectra for 23O and 24O are shown respectively in

Fig. 5.2. Also shown is the three-body decay energy spectrum for 24O with causality cuts

applied. The spectra shown require that the neutron time-of-flight fall between 50 and 150

ns. However, the requirement of good time-of-flight and multiplicity ≥ 2 is not sufficient

to separate two-neutron events from one-neutron events. To accomplish this, two cuts are

necessary: (1) the causality cut, and (2) a high threshold of 5 MeVee on each interaction.

The causality cuts are cuts on relative velocity V12 and distance D12 between the first

two interactions in MoNA. By requiring a large relative distance, nearby scatter is removed.

An additional cut on V12 will also remove scattering events as a scattered neutron will lose

energy. More information on the causality cuts can be found in Section 4.2.4.1.

The reason for this high threshold is because 22O is populated in multiple ways in this

experiment, with the dominant contribution coming from one-neutron knockout from 24O

which directly populates 23O as illustrated in Fig. 5.4. This results in an overwhelming

contribution of 1n events which need to be suppressed. The 5 MeVee threshold eliminates

events where a neutron interacts in the plastic and produces a γ-ray which can interact in

another location giving the appearance of two neutron interactions. It was observed through

simulation that applying this threshold greatly reduced the contribution of 1n scatter events

140

decayE0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.2

0.4

0.6

0.8

1

1n Decay

decayE0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Eff

icie

ncy

0

0.1

0.2

0.3

2n Decay

Figure 5.1: (Left) Acceptance of MoNA-LISA for a 1n decay as a function of Edecay. (Right)Acceptance for a 2n decay with causality cuts applied.

within the causality cuts.

The low-energy peak in 23O is evident in the two-body spectrum, corresponding to the

decay of a 5/2+ hole state. It is consistent with previous measurement [63]. The three-body

spectrum for 24O with causality cuts shows an apparent broad peak at ∼ 1 MeV which is

significantly higher than the previously reported value of ∼600 keV. However, here one must

be careful, as the acceptance of the causality cuts depends strongly on the configuration of

MoNA and LISA. Unlike the 1n efficiency, the 2n efficiency does not peak at zero decay

energy as shown in Fig. 5.1, and so a proper minimization is necessary to determine the

energy.

141

[MeV]decayE0 0.5 1 1.5 2 2.5 3

Co

un

ts

0

200

400

600

800

1000

1200

(a)

[MeV]decayE0 0.5 1 1.5 2 2.5 3

Co

un

ts

1

10

210

310

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

0

100

200

300

400

500

600

700

800

(b)

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

1

10

210

310

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

0

10

20

30

40

50

60

(c) Causality Cuts

Figure 5.2: (a) 1n decay energy spectra for 23O with contributions from neutron-knockoutand inelastic excitation. (b) The three-body decay energy for 22O + 2n for all multiplicities≥ 2. (c) The three-body decay energy with causality cuts applied. The inserts show alogarithmic view.

142

Figure 5.3 shows the three-body correlations for the 22O + 2n system in the T and

Y Jacobi coordinate systems. The spectra have the causality cuts applied, as well as an

additional requirement that E3body < 4 MeV.

Even without a fit, there are several features that indicate a sequential decay. The relative

energy in the Y-system, which represents the neutron-core energy, peaks around 0 and 1.

This is indicative of an uneven sequential decay where one neutron is high-energy, and the

other low. In addition the relative angle in the T-system peaks strongly at -1 and 1 with

a valley in between. This is also the result of two neutrons with disparate energies. The

T-system is constructed in the center-of-mass frame. Since one neutron imparts a bigger

kick than the other, when the less energetic particle is boosted into the frame of the more-

energetic one, its direction appears backward (even though it is isotropically emitted in the

n-core + n frame). This results in peaks at -1 and 1, or 0 and 180 degrees.

Note also that the spectra lack the features one would expect from a di-neutron decay.

The ratio Ex/ET in the T-system does not peak at 0, but rather at ∼ 1/2 implying that the

neutron-neutron energy is large relative to the total available energy. However, the spectra

do not contain 100% true 2n signals, and one must rely on simulation to estimate the amount

of contamination from 1n scatter.

As previously mentioned, 22O can be populated by multiple paths: (1) direct population

of 23O via 1n knockout from 24O , and (2) inelastic excitation to 24O∗ which decays by

two-neutron emission. Figure 5.4 illustrates these two population paths.

Since both paths may contribute, it is important to consider both the one and two-

neutron decay energy spectra in Fig. 5.2 simultaneously. This is done by a simultaneous

minimization of the log-likelihood ratio, −Ln[Λ] on (a) the 22O + 1n decay energy, (b)

the 22O + 2n decay energy, (c) and the 22O + 2n decay energy with causality cuts. This

143

0 0.2 0.4 0.6 0.8 1

Co

un

ts ­

T S

yste

m

0

10

20

30

40

50

60

­1 ­0.5 0 0.5 10

10

20

30

40

50

60

T/ExE0 0.2 0.4 0.6 0.8 1

Co

un

ts ­

Y S

yste

m

0

5

10

15

20

25

30

35

40

)kθcos(­1 ­0.5 0 0.5 1

0

5

10

15

20

25

30

35

40

Figure 5.3: Jacobi relative energy and angle spectra in the T and Y systems for the decayof 24O → 22O + 2n with the causality cuts applied and the requirement that Edecay < 4MeV.

method provides additional constraints over fitting each spectra independently by requiring

the model to appropriately reproduce the ratio of 1 to 2 multiplicity events. For example a

pure 1n model will fit the low-lying peak in 23O but will unable to also fit the causality cuts

provided a real 2n signal is present.

To allow for the direct population of 23O the decay of two previously reported states

was included: the low-lying sharp resonance at 45 keV [73, 68, 72, 63] and the first-excited

144

E [MeV]

0

1

2

22O 23O 24O

0+ S2n = 6.9 MeV5/2+

45 keV

3/2+

1/2+ Sn = 4.2 MeV

0+

(2+)(1+)

4.7 MeV

5.3 MeV

(2+, 4+)

24O(-1n) 24O(d, d′)

Figure 5.4: Level scheme for the population of unbound states in 23O and 24O from neutron-knockout and inelastic excitation. Hatched areas indicate approximate widths.

state at 1.3 MeV [74]. The one-neutron decays use the Breit-Wigner lineshape discussed

in Section 2.1.1. The two-neutron decay was modelled using the formalism of Volya [127],

detailed in Section 2.2.2.The best fit for the decay of 23O and 24O is shown in Fig. 5.5.

145

[MeV]decayE0 0.5 1 1.5 2 2.5 3

Co

un

ts

0

200

400

600

800

1000

1200

(a)

[MeV]decayE0 0.5 1 1.5 2 2.5 3

Co

un

ts

1

10

210

310

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

0

100

200

300

400

500

600

700

800

(b)

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

1

10

210

310

[MeV]decayE0 1 2 3 4 5 6

Co

un

ts

0

10

20

30

40

50

60

(c) Causality Cuts

Figure 5.5: (a) 1n decay energy spectra for 23O with contributions from neutron-knockoutand inelastic excitation. (b) The three-body decay energy for 22O + 2n for all multiplicities≥ 2. (c) The three-body decay energy with causality cuts applied. Direct population of the5/2+ state and 3/2+ state in 23O are shown in dashed-red and dashed-green respectively.The 2n component coming from the sequential decay of 24O is shown in dashed-blue anddecays through the 5/2+ state. The sum of all components is shown in black. The insertsshow a logarithmic view.

146

Parameter Deviation in E3body σ =√V [keV]

Input Beam θx in Sim. (±15 [mrad]) 14Target Eloss (±5% ∼ 10 [MeV]) 10Drift Length dL (1.56 vs. 1.7 [m]) 40CRDC1 X offset (±1 [mm]) 2CRDC2 X offset (±1 [mm]) 8Global tmean for MoNA-LISA (±0.2 [ns]) 6Total 45

Table 5.1: Error budget for the three-body decay energy. The dominant contribution is thedrift length, dL.

Using previously reported values for the states in 23O [73, 68, 72, 63, 74] we obtain

good agreement with the data. The best-fit for the three-body decay gives an energy of

E = 715±110(stat.)±45(sys.) keV, which agrees with previous measurement [63], although

the central value is approximately 100 keV higher. The systematic error was determined

by adjusting several calibration parameters and repeating the minimization to obtain the

fluctuations in the minimum energy. The error budget is given in Table 5.1.

Only an upper-limit can be placed on the width with Γ < 2 MeV, as the width is

dominated by the experimental resolution and the Breit-Wigner lineshape saturates at large

Γ. Within Volya’s description, even an input width of Γ = 6 MeV produced a resonance with

a FWHM of ∼ 400 keV. The best fit is shown using the single-particle width Γspdw = 120

keV. Using S2n = 6.93 ±0.12 MeV [8], we obtain an excitation energy for the three-body

state at 7.65 ± 0.2 MeV with respect to the ground state of 24O. No branching through

the 3/2+ state in 23O was necessary to fully describe the data. All three spectra in Figure

5.5 are well described by a single state in 24O. Even though the data are dominated by 1n

contributions from direct population of 23O, a one-neutron hypothesis cannot describe the

causality cuts as evidenced by its low amplitude in the causality cut spectrum of Fig. 5.5

(red line).

147

It is possible to fit the three-body energy with any of the two-neutron models considered in

this analysis. Since that spectrum only contains relative energy information, the orientation

of the nucleons is unimportant so long as their energy adds up to the three-body state. The

Jacobi correlations however, offer a powerful tool for discriminating between the different

possible decay modes. Figure 5.6 shows the experimental data in the T system next to

the predictions for each three-body model. Shown here are the same data in Figure 5.3

however now one can see how the relative enegy Ex/ET is correlated with angle cos(θ). The

amplitudes of the simulation are set to twice the integral of the three-body spectrum with

causality cuts.

It is immediately evident by Figure 5.6 that a di-neutron or phase-space model will be

unable to describe the data. Both models have the incorrect inflection in cos(θ), and do

not reproduce the bell shape in Ex/ET around ∼ 1/2. However, comparison to the phase-

space model is still useful, as it serves to illustrate what the “base-line” looks like in the

case where no correlations are present. The di-neutron is shown as well. Even though

it is not expected based on the structure of the energy levels, in principle the decay is

an interference of both a di-neutron and sequential emission. It’s inclusion demonstrates

that the observed correlations are distinct from di-neutron emission which other 2n unbound

nuclei are interpreted as emitting [51, 26, 54]. While the sequential model describes the valley

in cos(θ), and bell-shape in Ex/ET , it predicts the valley to be deeper than is observed. This

can be explained by contamination from 1n events from the decay of 23O.

Figure 5.9 shows the prediction of the best-fit of the decay energy spectra on top of the

observed Jacobi spectra. These spectra are reproduced and not fit. Here we assume the

decay is a sequential process passing through the low-lying intermediate state in 23O. The

agreement is very good. Shown in dashed-blue is the contribution from the sequential decay,

148

T/ExE

00.2

0.40.6

0.81)k

θcos(

­1­0.5

00.5

1

Co

un

ts

0

5

10

15

20

25

30

Exp.

T (a)

T/ExE

00.2

0.40.6

0.81)k

θcos(

­1­0.5

00.5

1

Co

un

ts

0

5

10

15

20

25

30

Sequential

T (b)

T/ExE

00.2

0.40.6

0.81)k

θcos(

­1­0.5

00.5

1

Co

un

ts

0

5

10

15

20

25

30

Di­neutron

T (c)

T/ExE

00.2

0.40.6

0.81)k

θcos(

­1­0.5

00.5

1

Co

un

ts

0

5

10

15

20

25

30

Phase­space

T (d)

Figure 5.6: Jacobi relative energy and angle spectra in the T system for the decay of 24O→22O + 2n with the causality cuts applied and the requirement that Edecay < 4 MeV. Shownfor comparison are simulations of several three-body decay modes. A sequential decay (b),a di-neutron decay with a = −18.7 fm (c), and (d) a phase-space decay. The amplitudes areset by twice the integral of the three-body spectrum with causality cuts.

149

and in gray is the contribution from the 1n decay of 23O. The observed shape of the Jacobi

spectra are what we expect give that the intermediate state in 23O is low-lying and narrow.

In the two-proton decay of 6Be [43] it was observed that the sequential decay mechanism

was suppressed until the decay energy satisfied the following relation:

E3body > 2 ∗ E2body + Γ2body

which is certainly fulfilled here. It is interesting however, that a full three-body calculation

is not necessary to describe the decay observed here. On the proton drip-line, several two-

proton emitting nuclei show signs of sequential emission competing with true three-body

processes [30, 43, 44].

The sequential decay is also supported within the shell model. The (d, d′) reaction mech-

anism will populate particle-hole states in 24O. Such a configuration is illustrated in Figure

5.7 and would be a particle-hole state with spin-parity 2+ or 4+. The USDB hamiltonian

predicts a 2+ and 4+ roughly 300 keV apart above the two-neutron separation energy. It is

possible that the observed resonance is a superposition of both the 2+ and 4+ states, how-

ever a single resonance is sufficient to describe the data. If the observed peak corresponds

to the 4+, then the agreement with the USDB interaction would be very good as shown in

Figure. 5.8. A 0+ is also predicted to be nearby in energy at 7.5 MeV. However, the 0+

would be a two-particle two-hole excitation which cannot be made by (d, d′). In addition,

another state has been observed above the two-neutron separation energy in 24O at 7.3 MeV.

This state however, was observed to undergo a one-neutron decay and was concluded to have

ν(1s1/2)−1ν(fp)1 configurations with negative parity [71].

In this picture, the first neutron decays from the ν0d3/2 orbital, and the second from

150

Figure 5.7: Neutron configurations for the two-neutron sequential decay. Filled circle repre-sent particles and faded circles represent holes. The 2+ or 4+ configuration of 24O is shownon the far right and is a particle-hole excitation. The 5/2+ state in 23O is a hole state whichdecays to the two-particle two-hole configuration of 22O which is a small component of theground state wavefunction.

the ν0d5/2, with the final-step being a decay to a two-particle two-hole configuration of the

ground state of 22O. Although the spectroscopic factor for the final step is small, it is finite,

as the ground state of 22O contains a mixture of the ν(1s1/2)2ν(0d5/2)−2 configuration at

roughly 14% as illustrated in Figure 5.7

It is expected that the neutrons have angular distributions reflective of the fact that

they both have ` = 2. It is at this point that Volya’s model breaks down, as it is assumed

that the neutrons originate from the same orbital, carry the same angular momentum, and

are emitted isotropically. At present, the angular distributions of the neutrons are left as

isotropic and the J+ of the state is tentatively assigned to 2+ or 4+. This does not affect

the decay energy measurement as it is a scalar. A full three-body calculation that properly

includes the angular distributions could provide valuable insight into the decay mechanism.

151

E [MeV]

Sn

S2n

0

4

6

8

2+

1+

(2+, 4+)

J−

0+0+

Exp. USDB

2+

1+

0+4+2+3+

24OFigure 5.8: Comparison of experimentally measured states in 24O with USDB shell modelpredictions. Data taken from Refs. [70, 71]. The state observed in the present work is shownin blue.

152

0 0.2 0.4 0.6 0.8 1

Co

un

ts ­

T S

yste

m

0

10

20

30

40

50

60

­1 ­0.5 0 0.5 10

10

20

30

40

50

60

T/ExE0 0.2 0.4 0.6 0.8 1

Co

un

ts ­

Y S

yste

m

0

5

10

15

20

25

30

35

40

)kθcos(­1 ­0.5 0 0.5 1

0

5

10

15

20

25

30

35

40

Figure 5.9: Jacobi relative energy and angle spectra in the T and Y systems for the decayof 24O → 22O + 2n with the causality cuts applied and the requirement that Edecay < 4

MeV. In dashed-blue is the sequential decay through the 5/2+ state in 23O. The remainingfalse 2n components from the 1n decay of 23O are shown in shaded-grey. The sum of bothcomponents is shown in solid-black

153

5.2 22N + 1n

In addition to observing the sequential decay of 24O, unbound states in 23N were also popu-

lated via one-proton knockout. The two-body decay energy for 23N is shown in Figure 5.10

after selection of 22N in the focal plane and requiring a valid neutron in MoNA-LISA.

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Figure 5.10: Two-body decay energy for 22N + 1n.

As of present, there are no reports of unbound states in 23N although it is known to have

a bound ground state [128] with a half-life of about 14 ms [129]. In addition, there are no

reports of any bound excited state. The data show two peaks around ∼ 100 keV and ∼ 1

MeV, both of which are less than the 2n separation threshold in 23N, which is at S2n = 3.07

MeV [8] and corresponds to 1.3 MeV in Figure 5.10. If the ∼ 1 MeV peak decays to the

ground state of 22N, it would correspond to a state at approximately 2.8 MeV with respect

to the ground state of 23N. Due to the drop-off in efficiency (Fig. 5.1), the intensity of the

∼ 1 MeV peak is nearly 3− 10 times higher than the lower-energy peak.

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Figure 5.11: Shell model predictions for 23N with the WBP and WBT Hamiltonians as wellas the Continuum Shell Model.

5.2.1 Interpretation

It is important to note that 22N has two bound excited states that the neutron decay of

23N could branch to. A study of in-beam γ-ray spectroscopy of 22N observed a 183 keV

and an 834 keV transition in coincidence, which have been interpreted as the level scheme

in Figure 5.11. Although the spin and parity of the ground and excited states of 22N are

tentative, both the WBTM and WBT interactions predict an ordering of 0−, 1−, and 2−

for the ground, first, and second excited states, respectively. It is then possible, that the

observed decay energy is not the true energy of a state in 23N, but rather the difference in

energy between a state in 23N and an excited state in 22N. In order to distinguish the two,

it would be necessary to have γ-ray detection around the target. Such detectors have been

used with MoNA in the past, e.g. CAESAR, however this measurement was not within the

original scope of the experiment. Thus, no γ-ray information is present in the current data.

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Because of this ambiguity, many level schemes and degeneracies are possible. At best, one

can only speculate while guided by theoretical calculations.

It is not likely to populate a 5/2− state in 23N by proton knockout from 24O, which has a

the ground state configuration of 0+. To populate a 5/2− state requires an ` = 3 component

of the wavefunction and the ground state configuration of 24O has none. A 3/2− state can be

populated by removal of a π0p1/2 proton, in which case the single proton left in the π0p1/2

orbit couples to a 2+ configuration of neutrons (ν1s1/2 ⊗ ν0d3/2). Additionally, a 3/2−

state is more easily made by simply removing a π0p3/2 proton. While more tightly bound,

there are a greater number of protons in the p3/2 orbital compared to the p1/2 orbital, and

populating the 3/2− in this way would not require re-arranging the neutrons. Calculations

with the WBP and WBT hamiltonian as well as the continuum shell model (CSM), predict

the lowest excited states in 23N to be 3/2− and 5/2− in the vicinity of 2 ∼ 4 MeV as shown

in Fig. 5.11. The first excited 1/2− does not appear until around 5 MeV of excitation. Thus

3/2− is the most likely candidate for the spin and parity of the state(s) populated in 23N.

If one assumes that the E ∼ 1 MeV peak does not originate from a transition to the

2− state in 22N, then the set of possible level schemes is reduced. This is a reasonable

assumption, since a decay to this state would imply observing a resonance above the two-

neutron separation threshold in 23N that undergoes a one-neutron decay. However, simply

being above S2n does not prevent 1n emission. For example, such a decay has been observed

in 24O [68] where a state above the two-neutron separation energy underwent a 1n decay to

23O. Under this assumption the possible ordering for these states is shown in Figure 5.12.

156

Figure 5.12: Possible level schemes that could give rise to the observed two-body decayenergy for 23N. Case (a) is the “Ground State Decay,” while the “Two State” scenario iscase (b), and the “Single State” case (e). The single state interpretation could also be twostates close together. Cases (c), (d), and (f) are excluded due to the weak intensity of the100 keV transition.

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5.2.1.1 Ground State Decay

First, in order to determine the energy, consider the “Ground State Decay” where each

peak consists of only a single contribution and represents an independent state in 23N. If we

assume the 1 MeV peak is not an overlap of two states, then the best-fit is shown in Figure

5.13. The best description was obtained with two ` = 2 Breit-Wigners at E1 = 100 ± 20

and E2 = 960 ± 30 keV. The width is dominated by the experimental resolution and does

not minimize. The χ2 asymptotes around 500 keV at a value within 1σ. For this reason, the

single-particle widths of Γ1 = 2 keV and Γ2 = 115 keV are used for the first and second 3/2−

respectively. This scenario, as well as many other possibilities in Fig. 5.12 can be excluded

by examining the spectroscopic overlaps C2S between 23N and 24O. These are summarized

in Table 5.2 for the WBT and WBP hamiltonians.

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Ground State Decay

Figure 5.13: Best fit of the two-body decay energy for 23N based on the “Ground StateDecay” interpretation. The purple curve indicates the 100 keV transition, the dahsed red isthe 960 keV transition. The 2n background is shown in shaded gray.

According to the WBP interaction, the lowest 3/2−1 has the strongest overlap, by about

a factor of ∼ 2 compared to the second 3/2−. The WBT interaction predicts slightly larger

overlap for the 3/2−2 . If we interpret the ∼ 100 keV peak as coming from a state below the

158

∼ 1 MeV peak, then we reach a contradiction between the data and shell model. Due to

our efficiency, the ∼ 1 MeV peak is approximately 3 ∼ 10 times more intense than the lower

energy peak implying C2S(3/2−2 ) > C2S(3/2−1 ), which is not what the WBP interaction

predicts. Although the WBT interaction does predict the overlap to the second 3/2− to

be greater, it is still about a factor of 4 too small. The intensity of the ∼ 100 keV peak

in any fit will always be smaller than the ∼ 1 MeV peak due to the acceptance of MoNA.

To be consistent with the spectroscopic factors the ∼ 100 keV transition can originate from

either the same state as the ∼ 1 MeV transition or a state above it. This leaves a couple

possibilities, referred to as the “Single State” and “Two State” scenarios: (1) A single state

at 1.1 MeV (or an unresolved doublet), and (2) a state at 1.1 MeV, and another below it at

960 keV.

5.2.1.2 Single State

The data can also be fully described by a single state at E = 1.1 MeV. In this scenario, the

∼ 100 keV transition is an ` = 0, 2 decay to the 2− state in 22N, and the observed peak

is a superposition of a 960 keV decay to the 1− state and a 1100 keV decay to the ground

state of 22N. Table 5.3 shows the ratio of intensities of each contribution in the fit, which is

WBP WBT

Ecalc Edecay Jπ 〈23N |24O〉 Ecalc Edecay Jπ 〈23N |24O〉(MeV) (MeV) C2S (MeV) (MeV) C2S

0 - 1/2−1 1.9328 0 - 1/2−1 1.9529

4.961 3.161 1/2−2 0.0025 5.257 3.457 1/2−2 0

3.610 1.810 3/2−1 1.4645 3.610 1.810 3/2−1 0.6893

4.525 2.725 3/2−2 0.6480 4.764 2.964 3/2−2 1.0483

Table 5.2: Spectroscopic overlaps for various states in 23N with the ground state of 24O.Edecay is calculated assuming the state decays directly to the ground state of 22N.

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Intesntiy Ratio WBP WBT Single State

Ii/I0− C2Si/C2S0− C2Si/C

2S0− 1100 keVI1−/I0− ∼ 0 0.002 4.52I2−/I0− 0.326 0.058 0.821

Table 5.3: Ratio of intensities in the single state interpretation compared to the equivalentratio formed from spectroscopic overlaps for possible initial states in 23N with final states in22N using the WBP and WBT interactions.

proportional to the partial width. The weakest intensity is the transition to the 2−, while

the other two decays (` = 0, and ` = 2) share their intensity in roughly a 4:1 ratio in favor

of the ` = 0 decay. The WBP interaction is consistent with such a scenario. Also compared

in Table 5.3 are the ratios of spectroscopic overlaps for 〈22N |23N〉 for both the WBP and

WBT interactions. Although they predict the s-wave decays (3/2− → 1−) to have almost

no overlap, a small spectroscopic factor does not eliminate the possibility. Case (e) of Figure

5.12 illustrates the level scheme in 23N for the “Single State” scenario.

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Figure 5.14: Best fit of the two-body decay energy for 23N based on the “Single State”interpretation. The purple curve indicates the 100 keV transition, the dahsed red is the 960keV transition, and the dashed blue is the 1100 keV transition. The 2n background is shownin shaded gray.

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Transition WBP WBT Two State G.S. Decay

Jπi → Jπf C2S 〈22N |23N〉 C2S 〈22N |23N〉 1100 keV + 950 keV 100 keV + 950 keV

3/2−1 → 0− 0.4792 0.6867 0.0209 (degenerate) 0.0049

3/2−2 → 0− 0.2926 0.0564 0.0054 0.025

3/2−1 → 1− ∼0 0.0013 - -

3/2−2 → 1− 0.0304 0.0220 - -

3/2−1 → 2− 0.1562 0.0401 - -

3/2−2 → 2− 0.0301 0.0492 0.0051 -

Table 5.4: Spectroscopic overlaps for possible initial states in 23N with final states in 22Nusing the WBP and WBT interactions. For comparison are the intensities for the best-fitsof the data.

5.2.1.3 Two State

There is another interpretation consistent with shell model. It is possible that the 100 keV

transition originates from a state above a separate state at 960 keV. In this case we observe

that the lowest 3/2− is most strongly populated and the second one is weakly populated.

This configuration would create another 960 keV transition which would be degenerate in

our spectrum, as well as a ∼ 700 keV transition. However, these would be s-wave decays.

Figure 5.15 shows the best fit in this scenario, which is similar to the “Ground State Decay”

interpretation but there is a small contribution from the 1.1 MeV decay. This case is referred

to as the “Two State” scenario. No s-wave component is necessary. Table 5.4 shows the

spectroscopic overlaps for possible initial states in 23N with final states in 22N compared to

the best-fit intensities of the “Ground State” and “Two State” scenarios. Both the WBP

and WBT interaction predict overlaps for the ` = 0 transitions to be very small < 0.002.

The small amplitude of the 1.1 MeV transition is also consistent with the WBT interactions

which predicts a small overlap for the decay of 3/2−2 → 0−. The strongest intensity is from

the 960 keV transition, which is interpreted as a direct decay to the ground state from the

lowest 3/2−1 and is consistent with both the WBP and WBT interactions.

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Two State

Figure 5.15: Best fit of the two-body decay energy for 23N based on the “Two State”interpretation. The purple curve indicates the 100 keV transition, the dahsed red is the 960keV transition, and the dashed blue is the 1100 keV transition. The 2n background is shownin shaded gray.

5.2.1.4 Background Discussion - Search for 24N

There is a high-energy tail in the data, and some background contribution is necessary. This

tail cannot be described by increasing the width of the E2 = 960 keV peak, as the width

of this distribution saturates. A variety of line-shapes can describe this background and

provide an adequate fit. The inclusion of another state at 3 MeV, a broad gaussian at 10

MeV, or a thermal distribution with T = 4 MeV all describe the high-energy tail.

The proton knockout reaction mechanism should be clean. The necessisty of some back-

ground in an otherwise clean reaction mechanism suggests the presence of another reaction

channel. In principle, charge-exchange from 24O to 24N could have occurred in this exper-

iment. 24N, being unbound, would decay to 23N which was unfortunately not within the

acceptance of the sweeper. However, if the charge-exchange populated a two-neutron un-

bound excited state then 22N could be produced creating a background in the one neutron

spectrum of 23N (Figure 5.10). Figure 5.16 shows the reconstructed two- and three-body

energies using either a 1n or 2n thermal background. The multiplicity is also shown for

162

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N + 1n22

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Multiplicity0 2 4 6 8 10

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Figure 5.16: Comparison between a 1n thermal background (Top) and a 2n background(Bottom). On the left is the two-body decay energy. The middle panels shown the three-body spectrum for 24N with causality cuts, and the far right panels show the multiplicity.The purple line is the E1 = 100 keV Breit-Wigner, the dashed red is the E2 = 960 keVresonance. The background contribution is shown in shaded gray.

comparison. The multiplicity in combination with the two- and three-body decay energies

has been shown to be a useful way of determining the number of neutrons emitted in a

decay. Previous studies with MoNA demonstrated this sensitivity in searches for 4n and 3n

emission in the reactions 14Be(-2p2n)10He [130], and 17C(-2p)15Be [131].

While the 1n thermal background reproduces the the two-body decay energy, it fails to

describe the observed counts in the three-body spectrum with causality cuts. In addition,

the simulation underpredicts multiplicities 3 and 4. A 2n thermal background can better

describe all three spectra simultaneously. The reduced χ2/ν for the causality-cut spectrum

is good at ∼ 7.7/5, compared to χ2/ν ∼ 27/5 for the 1n hypothesis, and the multiplicity

is better reproduced. A variety of two-neutron lineshapes were considered, including phase-

space and di-neutron decays, however they do not reproduce the two-body spectrum. The 2n

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thermal background, with T = 3 MeV, is used in this analysis as it provides a simultaneous

description of all observables.

5.2.2 Conclusions

It is important to note that the interactions discussed here do not reproduce the experimen-

tally observed energies in both 22N and 23N, although they are within 1 MeV. As 23N is at

the dripline, continuum effects and three-body forces may begin to play a significant role,

and these effects were not considered in this analysis. Experimentally, we cannot distinguish

between any number of cases or degeneracies that produce the energy differences observed in

the decay energy. Ultimately a repeat measurement with γ detection is necessary to clarify

the structure of 23N.

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Chapter 6

Summary and Conclusions

In this dissertation, measurements of neutron unbound states in 24O and 23N have been

reported. These states were populated by reactions from an 24O beam provided by the

Coupled Cyclotron Facility at the NSCL. Unbound states in 24O were populated by inelastic

excitation on a liquid deuterium target, and states in 23N were populated via one-proton

knockout. These states were measured by invariant mass spectroscopy, which required a

kinematically complete measurement of both the charged fragment and the neutrons emitted

in the decay of the unbound state. The resulting charged fragments were bent by the sweeper

magnet into a suite of charged particle detectors which measured their position and angle,

providing isotope separation. The neutrons, unaffected by the magnetic field, travelled

straight toward MoNA-LISA – an array of plastic scintillators that measured the neutron

position and time of flight. With the information provided by MoNA-LISA and the sweeper,

the invariant mass of the compound nucleus of interest was measured. In the case of two-

neutron emission, three-body correlations were examined to determine the decay mechanism.

Unbound states were observed in 23N for the first time. It is known that in this region

of the nuclear chart, Mayer and Jensen’s magic numbers breakdown and new shell-closures

appear. This shift has been attributed to the NN tensor force, three-body forces, and

continuum effects. 24O is doubly magic with Z = 8 and N = 16. 23N should also exhibit the

N = 16 shell gap although one expects it to be reduced. For example, the N = 14 sub-shell

gap in 22O was observed to disappear by the time one reaches 20C. Thus, identification of

165

states in 23N could help better constrain the tensor force and provide a better understanding

of shell evolution.

The two-body decay energy for 23N shows prominent peaks at E1 = 100 ± 20 keV and

E2 = 960±30 keV. 22N has two bound states that the decay of 23N could branch to, implying

that the observed decay does not necessarily populate the ground state of 22N. Rather it

could be a transition to an excited state in. However, due to the lack of γ-ray detection in

the experiment, one cannot make a definitive statement on the structure of 23N with the

current data. Shell model calculations with the WBP and WBT interactions lead to several

interpretations. A single state at 1.1 MeV above Sn, or 2.9 MeV with respect to the ground

state of 23N, is consistent with data and theory as well as two states at 2.9 MeV and 2.75

MeV, respectively. A repeat measurement with γ-ray detection is necessary to clarify the

structure of 23N.

In addition to 23N, a state above the two-neutron separation energy was observed in 24O.

It decays by emission of two-neutrons with a three-body energy of E3body = 715± 110 (stat)

±45 (sys) keV, placing it at E = 7.65 ± 0.2 MeV with respect to the ground state. The

three-body correlations in the T and Y Jacobi coordinate systems show clear evidence of

a sequential decay through a narrow state in 23O. A phase-space or di-neutron hypothesis

were unable to describe the observed correlations. This constitutes the first measurement of

a sequential decay, exposed by energy and angular three-body correlations in a 2n unbound

system. The measurement demonstrates the ability to distinguish experimentally, a di-

neutron signal from a different decay mode in addition to providing valuable information

about few-body physics at the neutron drip line. The three-body correlations were not

sensitive to the ` value of the decay leaving the spin-parity of this state undetermined. A

separate measurement is necessary to determine the angular momentum of this state.

166

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167

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